Iowa State University Capstones, Theses and Retrospective Theses and Dissertations Dissertations

1997 The ag mma-ray energy spectrum of the active galaxy Markarian 421 Jeffrey Alan Zweerink Iowa State University

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The gamma-ray energy spectriim of the active galaxy Markarian 421

by

Jeffrey Alan Zweerink

A dissertation submitted to the graduate faculty

in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY

Major: Astrophysics

Major Professor: Richard C. Lamb

Iowa State University Ames, Iowa

1997 Copyright © Jeffrey Alan Zweerink, 1997. All rights reserved. UMI Number: 9725474

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TABLE OF CONTENTS

ABSTRACT xiv

1 INTRODUCTION 1 1.1 Detection of Gamma Radiation 2 1.1.1 High Energy (HE) Radiation 2 1.1.2 Very High Energy (VHE) Radiation 3 1.2 Models of Active Galactic Nuclei o 1.3 Current Scientific Issues Addressable by Gamma-Ray Astronomy 7 1.3.1 AGN Issues 7 1.3.2 Other Issues 8 1.4 Organization of Dissertation 9

2 BACKGROUND 10 2.1 High Energy Gamma-Ray Astronomy 10 2.1.1 Development of the "Imaging" Technique 11 2.1.2 Current State of VHE Gamma-ray Detectors 12 2.2 Markarian 421 15

3 DATA ACQUISITION AND PREPARATION 19 3.1 The Telescope 19 3.2 Observing Modes 20 3.3 Data Acquisition and Storage 22 3.4 Data Reduction 23 3.4.1 Pedestal Subtraction and Flat-fielding 23 3.4.2 Cleaning 24 3.4.3 Parameterization 25

3.5 Data Analysis 28 iv

4 GAINS, NOISE AND PE/DC CONVERSION 31

4.1 Direct Measurement of PE/DC Conversion 31 4.1.1 Measurement of PMT Current Gains 31

4.1.2 Measurement of Signal Transmission 32 4.1.3 Calculating the PE/DC 33 4.2 Scaling the PE/DC from 1988-89 35

4.2.1 Digital Counts in the Second Highest PMT 35 4.2.2 Total Size of Shower 39

4.2.3 Compare Total Size of Largest Events 39 4.2.4 Separating the pe/dc and the reflectivity 39

5 METHOD FOR DETERMINING ENERGY SPECTRA 43 5.1 The Standard Analysis 43 5.1.1 Parameter Cuts 44 5.1.2 Energy Estimation 49

5.1.3 Collection Area 50 5.2 The Observations 52 5.2.1 Data Preparation 52 5.2.2 Parameter Distributions for the Data 53

5.2.3 Spectrum Extraction 53 5.2.4 Calculating Fluxes 56

6 ENERGY SPECTRUM FROM MARKARIAN 421-THE FLARE 59 6.1 The Markarian Flare Spectrum-Standard Analysis 59

6.1.1 Parameter Cuts, Energy Estimate and Collection Area 60 6.2 The Observations 60 6.2.1 Data Preparation 60 6.2.2 Parameter Distributions for the Data 62

6.2.3 Spectrum Extraction 62 6.3 The Extended Analysis-Removing the Upper Distance Cut 65

6.3.1 No Upper Distance Cut 66 6.3.2 Opening Up the Pass Band 69 6.3.3 Using the x Fits to the Parameters 70 6.3.4 Fitting the Parameters with a Cubic Polynomial 70 V

6.3.5 Summary of Extended Analysis 73

7 SPECTRAL VARIABILITY OF MARKARIAN 421 7.5 7.1 Choosing the Databases 7-5

7.2 Spectral Analysis 77 7.3 Sensitivity to Spectral Cutoff 79

8 CONCLUSIONS 81 8.1 Results from this Work 81 8.2 Future Directions 82

APPENDDC A CRAB AND MARKARIAN 421 DATABASES 84

APPENDEX B CALCULATION OF THE HILLAS PARAMETERS 90

BIBLIOGRAPHY 92 vi

LIST OF TABLES

Table 2.1 Current catalog of detected TeV gamma-ray sources 1-5

Table 2.2 Atmospheric Cherenkov Imaging Gamma Ray Observatories as of 1996 and the sources which each have detected. Sources where a DC e.xcess was detected are

included. Sources with only periodic emission are omitted 16

Table 3.1 Parameters and units calculated for each event 28 Table 3.2 Supercuts values forl995/96 29

Table 4.1 Current gains in units of 10® for 6 PMTs. Wop and G<,p are the normal operating voltage and corresponding gain. Giooo and Ggoo are the gains with the PMTs operating at lOOOV and 900V, respectively 33

Table 5.1 Supercuts values for 1988/89 44 Table 5.2 Extended Supercuts values for 1995/96 Crab Nebula data. The parameter fits

are shown in the brackets 46 Table 5.3 Bin by bin flux values for the 1995/96 Crab Nebula database 58

Table 6.1 E.xtended Supercuts values for 7 May 1996 Flare from Markarian 421. The parameter fits are shown in the braickets 60 Table 6.2 Counts for the ON runs and OFF run sets. The average OFF counts, statistical errors of the OFF, and the excess are shown in the last 3 columns. Only bins

with X > —0.4 are included in the totals 62 Table 6.3 Bin by bin flux values for the Flare from Markarian 421 66 vii

Table 6.4 Number of events passing gamma-ray cuts, bin-by-bin, for the ON runs and each of the 5 OFF run sets. The upper distance cut has been removed and the pass band set to accept 95% of the simulated gamma rays. The last 3 columns show

the average of the 5 OFF sets, the excess Non - (Noff), and the significance of the excess (cf. Eqn 5.14). The "Total" row is the sum of the number with

X > -0.4 69 Table 6.5 Number of events passing gamma-ray cuts, bin-by-bin, for the ON runs and each of the 5 OFF run sets. The upper distance cut has been removed and the pass

band set to accept 99% of the simulated gamma rays. The last 3 columns show the average of the 5 OFF sets, the excess Non — and the significance of the excess (cf. Eqn 5.14). The "Total" row is the sum of the number with X > —0.4 70 Table 6.6 Number of events passing gamma-ray cuts, bin-by-bin, for the ON runs and each of the 5 OFF run sets. The upper distance cut has been removed, the parameters fit with a cubic polynomial, and the pass band set to accept 99% of the simulated

gamma rays. The last 3 columns show the average of the 5 OFF sets, the excess Non ~{Noff), and the significance of the excess (cf. Eqn 5.14). The '^otal" row is the sum of the number with x > —0.4 72

Table 7.1 Results of the quick analysis for the combined, high and low databases 77 Table 7.2 Energy spectra derived for different Markarian 421 data sets taken during the 1995/96 observing season 77

Table A.l Data runs used to calculate the Crab energy spectrum for 1995/96 84 Table A.2 Data runs used to calculate the Markarian 421 energy spectrum for the Flare on 7 May 1996 86

Table A.3 Data runs used to calculate the Markarian 421 energy spectrum when it was in a high state during 1995/96. The Flare on 7 May 1996 is not included 87 Table A.4 Data runs used to calculate the Markarian 421 energy spectrum when it was in a low state during 1995/96 88 viii

LIST OF FIGURES

Figure 1.1 Multi-wavelength spectrum of Markarian 421 (adapted from Buckley et al. [9]).

The differential flux as a function of frequency, times the frequency, u, is plotted so that the area under the curve represents the power radiated. \ sub­ stantial fraction of the total power radiated by Markarian 421 is emitted at gamma-ray energies 4

Figure 1.2 Side view of the blazar AGN geometry. The black hole and accretion disk are on the left, the relativistic jet material is in the center, and the observer is on the right o

Figure 2.1 Simple schematic diagram of a particle shower caused by a high energy gamma

ray 11 Figure 2.2 Side views of a 0.35 TeV gamma-ray shower (left) and a 1.00 TeV cosmic ray

shower (right). The energies are chosen such that roughly equal amounts of total

light would be detected by a detector like the Whipple 10m telescope. Notice that the gamma-ray shower has much less transverse momentum and initiates much higher in the atmosphere than the cosmic ray shower 13 Figure 2.3 Light detected in the focal plane of the Whipple 10m telescope from a 0.35 TeV

gamma-ray shower (left) and a 1.00 TeV cosmic ray shower (right). Notice that the gamma-ray shower is much more compact and oriented towards the center

of the camera than the cosmic ray shower 14

Figure 3.1 Whipple 10m Telescope in its stowed position 20

Figure 3.2 Whipple lOm Telescope cameras for the 1988/89 (top) and 1995/96 (bottom)

seasons. Notice that for the 1995/96 camera, the outer 18 2" PMTs have been

replaced with 1" PMTs and light funnels have been added to collect the light that would have fallen between the PMTs 21 ix

Figure 3.3 Whipple 10m event at various levels of cleaning. This event would be selected

as a gamma-ray candidate by Supercuts 26 Figure 3.4 Whipple 10m event at various levels of cleaning. This event would be identified as a background event by Supercuts and rejected 27

Figure 3.5 Distribution of alpha values for two different Markarian 421 datasets. The solid line is for the ON run, and the dashed line is for the OFF run. The top plot

is 848 minutes of data taken between December 1995 and February 1996. The bottom plot is 108 minutes of data taken during the Flare on 7 May 1996. For

both cases there is a clear excess at small values of alpha 30

Figure 4.1 Schematic diagram of setup used to measure PMT current gains 32 Figure 4.2 Schematic diagram of PMT signal path from the PMTs to the ADCs 34 Figure 4.3 Digital count spectra are plotted for the P', o"", lO"* and 20"' highest PMTs

from each event. Differential (top) and integral (bottom) spectra are shown. The differential spectra are well described by a power law with index -2.33 giving integral spectra with index -1.33 36 Figure 4.4 Simple graphic illustrating how to determine the ratio of throughputs, or, for

seasons A and B 38 Figure 4.5 Three different techniques of scaling the pe/dc from one epoch to another. The top plot shows the integral digital count spectrum of the second highest PMT in events per second, and the middle plot shows the digital count spectrum of the total size of the shower in events per minute. The bottom two plots show

the log of the size of largest events for 1988/89 and 1995/96 (left) and the log of the ratio (right) 40 Figure 4.6 The top plot shows the integral digital count spectrum for runs taken with and without cones on 7 June 1996. The bottom plot compares the log of the total

size for the largest events (left) and the log of the ratio (right) for the same two runs 42

Figure 5.1 Average parameter values of simulated gamma rays as a function of the log of the energy where the error bars are standard deviations. The shaded areas denote

the pass bands of Supercuts. For width and length, Supercuts' sensitivity to gamma rays decreases markedly with increasing energy 45 Figure 5.2 Average parameter values as a function of LogS for the standard analysis. The

error in the mean is shown (the highest and lowest bin only have one event). The solid line is the fit and the dashed lines are the pass bands that select 95% of the simulated gamma rays. Supercuts is shown as the shaded region for

comparison. The poor fits at larger values of LogS (higher energies) are due to ADC saturation effects

Figure 5.3 Average parameter values as a function of LogS for the standard analysis. The solid circles are with PMTs above 1024 digital counts truncated to 1024 digital counts. The open circles have no truncation are fit well by a quadratic up to LogS > 4.5

Figure 5.4 Histogram of the difference between the log of the primary energy, x and the log of the estimated energy, x. Only Monte Carlo gamma rays passing the cuts used in the standard analysis are included. The solid curve is a Gaussian function

with <7re,=0.16 Figure 5.5 Collection area as a function of energy for the standard analysis. The solid circles show the trigger collection area while the open circles show the collection area for the simulated gamma rays that pass the parameter cuts. The solid line shows the fit to the cut collection area given by Eqn. 5.10 Figure 5.6 Comparison of Monte Carlo and data parameter distributions with gamma-ray cuts applied. (The alpha, length and width distributions have only the other two cuts applied, e.g., the alpha plot is cut on length and width.) Monte Carlo events are distributed with a -2.4 power law. Both data and Monte Carlo events have a cut of 0.6° < dist < 1.0° to increase the energy resolution. The solid lines and error bars are the data and the squares are Monte Carlos

Figure 5.7 Contours of x' for the standard analysis using. The solid contours indicate an increment of ,v" by 1. The dashed contour corresponds to ein increase of x" by 2.3 which denotes the statistical error bars Figure 5.8 The top plot shows the collection area (open circles) and the fit to the collection area given by Eqn. 5.10 (solid line). The dashed line is the modified area using a resolution function of

Figure 5.9 Energy spectrum of the Crab Nebula from the 1995/96 observing season. The line is the fit given in Eqn. 5.15 .58

Figure 6.1 Collection area as a function of energy for the 7 May 1996 Flare from Markarian 421. The solid circles show the trigger collection area while the open circles show

the collection area for the simulated gamma rays that pass the parameter cuts. 61 Figure 6.2 Comparison of Monte Carlo and data parameter distributions with gamma-ray cuts applied. The solid lines and error bars are data and the squares are Monte Carlos. The alpha, length and width distributions have only the other two cuts applied, e.g., the alpha plot is cut on length and width. Monte Carlo events are

distributed with a -2.4 power law. Both data and Monte Carlo events have a distance cut of 0.6° < dist < 1.0® to increase the energy resolution 63 Figure 6.3 Contours of y" for the standard analysis. The solid contours indicate an incre­

ment of x" by 1. The dashed contour corresponds to an increase of by 2.3 and denotes the statistical error bars 64 Figure 6.4 Energy spectrum of Markarian 421 during the 7 May 1996 Flare. The line is the fit given in Eqn. 6.1 65 Figure 6.5 Collection area eis a function of energy for the extended analysis. The solid circles show the trigger collection area while the open circles show the collection area for the parameter cuts that pass 95% of the simulated gamma rays 67 Figure 6.6 Average parameter values as a function of LogS for the extended analysis. Errors in the mean are shown, but the highest and lowest bin have only one event. The solid line in the fit and the dashed (dotted) lines are the pass bands that select 95% (99%) of the simulated gamma rays 68 Figure 6.7 Quadratic parameters fits as a function of x (left) and cubic fit to LogS (right) for the extended analysis shown. Here, the error bars are deviations from the

average. The dashed lines are the pass bands that select 99% of the simulated gamma rays. Note the better fits at larger values of LogS and x 71

Figure 6.8 Final energy spectrum of Markarian 421. The flux points are obtained using quadratic fits to the parameters with pass bands that accept 95% of the gamma rays. The solid line is the fit from the standard analysis (see Eqn. 6.1) 73 xii

Figure 6.9 The integral significance as a function of x. The data comes from using quadratic fits to the parameters with pass bands that accept 95% of the gamma rays. The spectrum extends smoothly up to 6 TeV, where statistics run out, with no evidence for a cutoff. 74

Figure 7.1 Histogram of the nightly gamma-ray rates for Markarian 421 during the 1995/96

observing season. Only data taken in ON/OFF mode in good weather with no indication of telescope problems are included 76

Figure 7.2 Energy spectrum of Markarian 421 for the combined database (top) and the high and low databases (bottom). The solid line shows the spectrum for the high state, and the dashed line shows the spectrum of the low state 78 Figure 7.3 Energy spectrum of the simulated signal injected into the Markarian 421 OFF runs. The lines are fits where all data points are included (dashed) and where only the points below 2 TeV are included (solid). Both are good matches to the

data 80

Figure B.l Graphical representation of the Hillas parameters calculated for each event. . . 90 xiii

ACKNOWLEDGMENTS

I would not have been able to accomplish this work without the assistance of a number of people.

First I would like to thank Dr. Elichard Lamb and his wife Jane. I appreciate his patient and able guidance and his concern for my growth as a professional and a person. Under Dr. Lamb's tutelage,

I believe I have become a much better scientist as well as communicator. Jane also provided much needed support and encouragement for my wife during a rather trying time.

I would also like to acknowledge Dr. David Carter-Lewis for his help in keeping me on track during the last year of my research. His persistent and patient direction have help me become a more thorough critic of my own work.

I cannot adequately e.xpress my appreciation for the love and encouragement my parents have given me and my family. They have devoted much of their life to instilling in my brothers and me the truly important values in life-a strong faith in the Creator and Sustainer of this world, a deep commitment to family, a gracious and generous attitude towards others. Their prayers and wisdom have enabled my family to grow much stronger during my graduate tenure. Of course I would not have completed this task without the abundant support of my wife . During the long hours of work and many weeks of my traveling, her attitude has been a source of encouragement and blessing for me. She has picked up much of the slack so that I could devote the time necessary to finish this research. The words of Solomon ring true, "An excellent wife is the crown of her husband." Thank you Lisa for being such a beautiful crown. The more I learn about God's marvelous creation, the more I concur with the psalmist:

The heavens are telling of the glory of God; and their expanse is declaring the work of His hands. Psalm 19:1 xiv

ABSTRACT

This is a study of the very high energy gamma-ray emission from Markarian 421. The data were taken by the Whipple Observatory 10 meter imaging atmospheric Cherenkov telescope (lACT) during the 1995/96 observing season. A method of extracting energy spectra using data obtained from lACTs has been previously developed at Iowa State University. This method is reviewed in the context of finding the spectrum of the Crab Nebula, the "standard candle" of very high energy gamma-ray astronomy. One important quantity that sets the energy scale of the Whipple 10 meter telescope is the electronic gain. This quantity has been determined by a direct measurement of the telescope electronics and by scaling previously measured values to the current observing season. Once the spectrum of the Crab Nebula during the 1995/96 observing season is found, the method is then applied to the Markarian 421 data. Of particular interest is a very intense flare observed on 7 May 1996. After the energy spectrum during the flare is found, I extend the method to investigate the high energy end of the spectrum. DeJager, Stecker and Salamon predict that the spectrum of Markarian 421 will cutoff between 1-10 TeV due to absorption by extragalactic background light. No cutoff is observed from the flare up to 6 TeV where statistics run out. Instead, the derived spectrum is more consistent with that predicted by MacMinn and Primack which gradually steepens between 0.3-10 TeV and then cuts off above 10 TeV. Energy spectra were found from the rest of the 1995/96 Markarian 421 data after dividing the data into periods of high and low emission. The low state spectrum is slightly steeper than the high state spectrum.

However the difference, because of the limited number of photons collected during the low periods, is not statistically significant, being only 1.2er. 1

1 INTRODUCTION

One of the long-standing problems in astronomy has been the origin of the cosmic ray flux that

bombards the atmosphere of the earth at a rate of ~ 1000 particles/m-/s. With energies that extend beyond 10"° eV, the physical phenomena occurring at cosmic ray production sites are well beyond anything producible in terrestrial laboratories. Since their identification over 80 years ago by Victor Hess [40] the composition, flux and spectra have been well measured. However, we have no direct evidence of their origin. Because cosmic rays are charged, they are deflected by the solar, galactic and intergalactic magnetic fields. The trajectories are altered to the point that below ~ 10'® eV the anisotropy of the cosmic rays detected at the top of the atmosphere is less than 1 in 10^. [40] Thus, for all but the highest energy cosmic rays, the arrival direction is unrelated to the source direction. However, many of the proposed mechanisms for producing cosmic rays will also generate gamma rays, which are unaffected by intervening magnetic fields. Thus, detecting and characterizing sources of gamma radiation should give greater insight into the origins of cosmic rays. Teshima [64] outlines a three component model to explain the measured cosmic ray spectrum. Below 10^'* eV the cosmic rays are produced by galactic supernova remnants (SNR). From 10^'^ — 10'® eV the cosmic rays are produced by some other galactic mechanism, and above 10'® eV the cosmic rays are extragalactic. In keeping with this picture, the focus of gamma-ray experiments until the early 1990's was on galactic objects. X-ray binary systems (Cygnus X-1, Hercules X-1, Vela X-1, etc.), radio pulsars

(Crab, Vela, Geminga, etc.), and SNR (7 Cygni, IC 443, W44, etc.) were the primary targets. Drury [23] outlines a simple argument why these objects, particularly SNR, are suspected of producing the galactic cosmic ray flux. The energy required to sustain the flux against loss by escape, nuclear interactions and ionization is estimated to be of order 10*" erg/s. The mechanical energy deposited into the galaxy by a supernova is of order 10®' erg. With a rate of one every 30 years this provides lO''" erg/s. If a mechanism exists for channeling 10% of this energy into cosmic rays, supernovae could easily provide the mechanical energy necessary to sustain the galactic cosmic ray flux. Enrico Fermi proposed such a •2

mechanism in 1949 [25] noting that particles will be accelerated when they encounter the shock front

produced where the supernova ejecta collides with the interstellar medium. Gaisser [27] gives a more thorough description of Fermi acceleration as well as a more complete discussion of how these types of objects can produce cosmic rays.

1.1 Detection of Gamma Radiation

Although mechanisms exist for producing cosmic rays, the intervening magnetic fields make it im­ possible to directly detect sources of cosmic rays. However, as mentioned above, cosmic ray sources should also produce gamma rays which, because they are uncharged, are unaffected by the magnetic fields. In searching for gamma radiation from these objects, different techniques are used depending on the energies one is trying to detect. Here I will focus on two energy ranges for which successful detectors have been in operation during the past decade. These are 10® — 10^° eV (0.1-10 GeV) using spark chamber detectors in space and 10^^ — 10^^ eV (0.1-10 TeV) using ground-based air Cherenkov telescopes.

1.1.1 High Energy (HE) Radiation

The most successful instrument designed to detect gamma radiation in the energy range 10®—10'° eV is the space-based Energetic Gamma-Ray Experiment Telescope (EGRET) of the Compton Gamma Ray Observatory (CGRO). In the first two years of operation after its launch in April 1991 EGRET detected 129 sources of gamma-ray emission above 100 MeV. [65] These included one bright solar flare, the Large Magellanic Cloud, five pulsars, 40 high-confidence identifications of Active Galactic Nuclei (AGN), 11 more AGN with lower confidence, and 71 sources not yet identified with known objects. As with earlier satellite gamma-ray experiments, many of the sources detected are not identified with known objects at other wavelengths.' This is due in part to the large error boxes associated with the satellite experiments. However, it might be indicative of sources which are bright in gamma rays but not at lower energies. What is surprising about the identified sources is the abundance of extragalactic objects compared to galactic objects. With 51 identified AGN, a minimum of 40% of the objects detected by EGRET are extragalactic with the frsurtion possibly being much higher.

Another remarkable feature of the observed AGN is the amount of power radiated at gamma-ray energies. Figure 1.1 shows the spectrum of the AGN Markarian 421 plotted over 18 decades in energy.

'Only six of the 25 objects detected by the COS-B satellite in 1975 have been identified with counterparts at other wavelengths. 3

The differential flux as a function of frequency, F„, times the frequency, u, is plotted so that the area

under the curve is the amount of power radiated. Gamma rays with energy greater than 100 MeV account for nearly half of the power radiated from Markarian 421. This feature is common among the other EGRET detected AGN, often with the gamma radiation dominating that of all other wavelengths.

1.1.2 Very High Energy (VHE) Radiation

The prototype instrument for observing gamma radiation between 10^^ — 10^^ eV is the Whipple

Observatory imaging atmospheric Cherenkov telescope. With the current camera it is the most sensitive telescope operating in this energy range. Using a less sensitive camera, Weekes et al. [67] reported the detection of the Crab Nebula at a 9

Interestingly, but in line with the HE observations of EGRET, the ne.xt 3 sources detected by the Whipple Collaboration are extragalactic objects- the AGN Markarian 421 [53], Markarian 501 [55] and 1ES2344 (see discussion in [69]). It should be noted that 3 galactic objects in the southern hemisphere have been detected- PSR B1706-44 [35] and the Vela Nebula [73] by the CANGAROO group and GRS 1915+105 [1] by the HEGRA collaboration. VHE gamma-ray observations are beginning to test the premise that SNR produce the cosmic ray flu.x below 10^'' eV. The 3 SNR that have been detected so far-the Crab, Vela and PSR B17Q6-44-are all plerions, i.e., remnants with a radio pulsar at their center. The emission from plerions is driven by the electrons produced by the pulsar, and as such, these objects are not expected to contribute significantly to the cosmic ray flux. However, shell-type SNR, where emission is driven by the collision of the supernova ejecta with the interstellar medium, are e.xpected to produce cosmic rays. The non- detections of these objects in VHE gamma rays provide the strongest constraints on the contribution of

SNR to the cosmic ray flux. As described by Hillas [31], the gamma-ray flux upper limits placed on 4 shell-type SNR fall below the predictions of current models. However, given the number of uncertainties in these predictions, most models are still consistent with the upper limits. More sensitive observations of this class of objects are necessary to definitively suddress this issue. The overwhelming fraction of identified sources at gamma-ray energies are AGN. As a result, the focus of gamma-ray astronomy has shifted towards extragalactic objects. While not believed to con­ tribute significantly to the cosmic ray flux, many important scientific issues can be addressed by the study of AGN. In this light, I will give a description of the prevailing models of AGN and discuss how HE and VHE gamma-ray observations can contribute to their understanding. 4

-8 JO I I I I I I i I I I I I I I I I I I I I I I I I I I i I I I I I I I I I—I r cs 0 May 7, 1996 'e * April 26, 1995 (approx.) o • May 15, 1994 (approx.) -9 >2.10 O 1977 to 1995 > tu

-10 10 . i •

0 <;?ts -11 u 10

-12 10 £ V V -13 10 t • A -K

-14 I I I I ' I I I I I I I ' I ' ' ' I ' ' ' I I ' ' I I i_j I I I 1 I I ' I I I 10 10 12 14 16 18 20 22 24 26 28 Log(v) (Hz)

Figure 1.1 Multi-wavelength spectrum of Markarian 421 (adapted from Buck­ ley et al. [9]). The differential flux as a function of frequency, times the frequency, u, is plotted so that the area under the curve represents the power radiated. A substantial fraction of the total power radiated by Markarian 421 is emitted at gamma-ray energies 0

Active Galactic Nucleus

Matter from the accretion disk will fall onto the Black Hole Observer

Very Relatlvistic Jet Material

role i^^tion. otation Axis

Figure 1.2 Side view of the blazar AGN geometry. The black hole and accre­ tion disk are on the left, the relativistic jet material is in the center, and the observer is on the right.

1.2 Models of Active Galactic Nuclei

All of the AGN detected by EGRET and Whipple belong to a small subset of objects called blazars. These are characterized by flat, high-frequency radio spectra, strong optical polarization and rapid optical variability. Often blazars exhibit apparent superluminal behavior. The prevailing picture of AGN is a supermassive black hole accreting matter from a disk, with opposing jets of relativistic material emitted perpendicular to the accretion disk (see Figure 1.2). In a simple unified model, the AGN classification depends on the observer's orientation relative to the jet. Blazars are believed to be viewed at small angles relative to the jet axis. For a thorough description of AGN taxonomy see Dermer and Schlickeiser [21] or Antonucci [2]. It is generally accepted that the gamma-ray emission from blazars is associated with the jets. The day-scale and hour-scale variability seen by EGRET and Whipple implies an emission region on the order of a light day in size. However, if the emission originated near the central black hole, the total luminosity implied would be as high as 10''® erg/s for some AGN. Given this luminosity and the size of the emission region, Schlickeiser showed that the optical depth for photons greater than 1 MeV interacting, i.e.,

7+7—+ (1.1) is much greater than unity. [60] However, if the emission region is moving relativistically with the jet, 6

two effects occur that reduce the 77 optical depth.

First, the relativistic beaming that occurs reduces the true luminosity by 10- —10^ from that derived assuming isotropic emission. This means that there are fewer photons available for interaction. Second, the observed time-scale of variability is shortened compared to the intrinsic time-scale. Consider an

emission region moving with velocity v which emits two flashes at times ty and <2- The intrinsic timescale is = <2 —'i- To an observer at an angle 0 to the line of motion, the source is vcos(9)*At closer when the second flash is emitted. Thus, the observed time between the flashes is <2 — vcos(6) * [At)/c — ti, or S * Ai, where J = 1 — 0cos(O). This means that the emission region is a factor of S larger than if

the emission region is at rest. The smaller luminosity and larger emission region reduce the 77 optical depth below unity.

While it is generally agreed that the gamma-ray emission originates in the jets, many different production mechanisms have been proposed falling broadly into two categories. The first, more widely accepted category assumes that the jet is predominantly leptonic. The gamma-ray emission is produced

by inverse Compton scattering of photons off of the relativistic electrons/positrons in the jet. This process involves photon-electron scattering where energy is transferred from the electron to the photon, thus the name inverse Compton. Within this picture the models differ further depending on the source of the scattered photons. In the synchrotron self-Compton model (SSC) [44] the seed photons are synchrotron radiation from the electron/positron population of the jet. Dermer and Schlickeiser [22] proposed another model where the scattered photons originate from the accretion disk. In yet another model by Sikora, Begelman and Rees [62], the jet moves through an ambient field of reprocessed photons produced external to the central nucleus. This ambient field provides the seed photons that get Compton scattered to gamma-ray energies. The second category has jets comprised of both hadronic and leptonic material and are referred to as

the "proton blazars". In this model, Mannheim [43] suggests that protons accelerated up to 10^' GeV are responsible for the gamma-ray emission. Protons will interact with ambient photons via

p + 7 —> -t- p (1.2)

p + 7 —>• e'*' + e~+p (1.3)

The it" will decay to 2 gamma rays which will then be absorbed via Eqn. 1.1 leading to a particle/photon cascade. Below some energy the optical depth for Eqn. 1.1 falls below unity and gamma rays are emitted from the jet. i

1.3 Current Scientific Issues Addressable by Gamma-Ray Astronomy

1.3.1 AGN Issues

While the preponderance of cosmic rays below 10^® eV are believed to be of galactic origin, and thus unrelated to AGN, gamma-ray observations of these extragalactic objects address a number of

important scientific issues. Detailed energy spectra of these AGN from the HE to VHE regimes will be needed to adequately resolve these issues.

It is difficult to discriminate between the various AGN models based on current measurements. Observations at different energies have been made during different epochs, but all AGN detected above 100 MeV are variable. Because of the exotic processes required to produce high energy gamma rays, observations above 100 MeV can place some of the tightest constraints on the various models. This is particularly true when gamma-ray observations are coupled with simultaneous lower energy observa­ tions. With rapid variability seen at some wavelengths yet not at others, some models could be rejected by detailed, simultaneous measurement of energy spectra during quiescent and flaring states. Of particular observational and theoretical interest in this pursuit is the energy gap between 10 GeV (upper EGRET range) and 200 GeV (lower Whipple range). If the spectra of the 50-1- AGN measured by EGRET are extrapolated to 250 GeV, the flux for many of them is well above the sensitivity of the Whipple telescope. However, Whipple detects only one of the AGN detected by EGRET. While it is obvious that the fiux from these sources cuts off in this energy gap, it is not known whether this cutoff is intrinsic to the AGN or due to external absorption. Proposed gamma-ray detectors that will close this gap (the space-borne instruments like GLAST [6] and AGATE [49] and ground based detectors like

VERITAS [70], MAGIC [7], STACEE [50], etc.) should be able to make the decisive flux and spectral measurements to pin down the cause of the energy cutoffs.

If the intrinsic spectra of a number of these AGN extend to TeV energies another issue with far- reaching implications can be addressed. As pointed out by MacMinn and Primack [42], a tight constraint on the epoch of galaxy formation would result from a measurement of the extragalactic background light (EBL). Currently, only upper limits are known in the near infrared region. Stecker, DeJager and Salamon [63] describe how VHE spectrum measurements can be used to determine the EBL in the near infrared and Biller et al. [4] find the most stringent limits between 10-12/im using VHE observations of Markarian 421.

To understand the contribution of VHE gamma-ray astronomy in measuring the EBL it is necessary to look at the photon-photon interaction of Eqn 1.1. The cross-section for this interaction peaks around 8

an energy in the center of mass equivalent to twice the square of electron mass energy. This corresponds to photons of energy

(1.4)

or about 2/im for TeV gamma rays. Thus, the near infrared intensity of the EBL can be determined from the attenuation of TeV gamma rays. For accurate determination, many spectra from sources of varied redshift whose intrinsic spectra extend to the VHE regime need to be measured. This work

presents a first measurement of the spectrum of Markarian 421 at TeV energies.

Because of its distance, emission from Markarian 421 can be used to probe the EBL by looking at the high energy end of its spectrum. The highest energy gamma rays detected without evidence of absorption set the strongest upper limits on the IR region of the EBL. This issue will be addressed in part by this work.

1.3.2 Other Issues

As VHE instruments become more sensitive, unresolved issues related to SNR will be settled. If SNR are the sources of cosmic ray, they will be detected in gamma rays and the shock acceleration mechanism verified. Determining which types of SNR shine in gamma rays will tell which SNR con­ tribute significantly to the galactic cosmic ray flux. If they are not detected, Fermi acceleration at SNR shock fronts will be ruled out as the mechanism for producing the cosmic ray flux below 10''' eV.

Other interesting questions can be answered by VHE measurements. The origin of the bursts detected by the Burst And Transient Source Experiment (BATSE) on the CGRO is still unresolved. The

1000+ bursts detected by BATSE have an isotropic distribution on the sky. However, the distribution is not consistent with a population uniform in distance; one is clearly seeing a fall-off at large distances. Only two possibilities are consistent with such a distribution. Either they are at cosmological distances or within a large extended halo in our galcixy. Because of the 77 —> e+e" process discussed earlier, the cosmological origin of the bursts would come under serious question if any of these bursts were detected at TeV energies.

Some models of primordial black holes (PBH's) predict a burst of TeV gamma rays as the hole evaporates. It may be possible to detect these evaporations with current and future ground-based gamma-ray telescopes. While Connaughton et al. [18] searched the Whipple database from 1992-1995 9 and found no evidence for a PBH evaporation, tliese are rare events with poorly understood physics and need to be investigated more extensively.

If the VERITAS detector is built, there exists the possibility of completing an all-sky survey in the

VHE regime. Similar to all-sky surveys at other energies, we can expect a greater understanding of current gamma-ray sources. Likely, we will also discover new phenomena from previously undetected classes of objects.

1.4 Organization of Dissertation

The focus of this work is a determination of the VHE spectrum of Markarian 421. Chapter 2 briefly describes the history and development of VHE gamma-ray astronomy and as well as discussing some ob­ servations of Markatian 421 at various wavelengths. Chapter 3 discusses the data acquisition, reduction and analysis. As this has been described quite well for the 1988/89 observing season by Mohanty [47], the focus will be on the changes that have been made through the 1995/96 observing season. Chapter 4 addresses some issues regarding the calibration of the telescope. Chapter 5 gives a description of the procedure to extract spectra from data taken by the Whipple 10 meter Telescope concentrating on the Crab Nebula database accumulated during the 1995/96 observing season. Chapters 6 and 7 apply the technique to extract spectra from Markarian 421 during the Flare on 7 May 1996 and to other Markar­ ian 421 databases acquired during the 1995/96 observing season. Finally, Chapter 8 ties everything together and discusses some implications of the results. Future observations and research directions are also given. 10

2 BACKGROUND

Cosmic rays and gamma rays deposit their energy in the atmosphere as they move towards the

ground. For energies greater than a few GeV, the bulk of this energy produces a shower of relativistic particles as depicted for a gamma ray in Figure 2.1. For a cosmic ray there will predominantly be nuclear interactions producing pions and other nucleon secondaries. In 1959, Cocconi [16] predicted that number of air showers produced by gamma rays coming from the Crab Nebula should be detectable above the cosmic ray background. In his model of the Crab

Nebula, pions are produced from the protons ejected in the original supernova event. Each charged 7r* decays to an electron and each tt" produces 2 gamma rays. Thus, for each electron of a given energy, one would expect a gamma ray of similar energy. He estimated the energy spectrum of the electrons from the visual magnitude of polarized light and the magnetic field of the Crab Nebula. If all of the electrons came from pion decays, he predicted that the gamma-ray signal above 1 TeV from the Crab Nebula would be 3 orders of magnitude above the background. Based on this prediction, attempts were

made to measure the gamma-ray flux from the Crab Nebula, and the field of TeV gamma-ray astronomy was born. [68]

Cocconi's prediction was based on detectors that were sensitive to the actual particles produced

in the air shower. In 1955, Galbraith and Jelley predicted and demonstrated that it was possible to detect the Cherenkov light from these particle showers. [28],[33] Their experiments used small optical

reflectors with a photomultiplier tube (PMT) at the focus. Since this type of detector is better suited to observing discreet sources, Galbraith and Jelley's detector served as the prototype for virtually every

VHE gamma-ray experiment.

2.1 High Energy Gamma-Ray Astronomy

Most early experiments to detect high energy gamma rays from the Crab Nebula looked for a directional anisotropy. The number of events recorded when the detector was pointed at the Nebula and at a control region were compared. The first serious attempt to measure gamma rays from the Crab II

Mean.en^gy per Distance through particle/fmoton medium

E/2 2R

EV4 3R

E/8 4R

E„/16 5R

Figure 2.1 Simple schematic diagram of a particle shower caused by a high energy gamma ray.

Nebula was by a group from the Lebedev Institute in Moscow. They used an array of 12 telescopes of 1.5m aperture arranged on four parallel mounts. [15] The sensitivity of the experiment was two orders of magnitude lower than the flux predicted by Cocconi. Unfortunately, Cocconi's mechanism for producing gamma rays was incorrect, and his prediction was three orders of magnitude too high. In retrospect, we realize the near hopelessness of detecting a simple directional anisotropy. Let's consider a source roughly as bright as the Crab Nebula-the brightest, steady source of TeV gamma rays known. The Crab Nebula emits approximately photonsfm-fs above 1 TeV. For a typical detector with an effective collection area of ~ 5 x lO^'m*, this translates to 50 showers in 10'' seconds of observation. With an effective angular resolution of 1®, a factor of 10^ more cosmic ray showers will be recorded. To detect this source at the 5

2.1.1 Development of the "Imaging" Technique

While there were discrepancies between early simulations by various groups, it was clear that there were marked differences between gamma-ray and cosmic ray showers (see Hillas [30], Plyasheshnikov and Bignami [51], and Macomb and Lamb [41]). Due to the lack of nuclear interactions, the gamma-ray 12

shower has much less transverse momentum and is therefore more compact than the cosmic ray shower.

This is clearly seen in Figure 2.2. Also, the gamma-ray shower interacts higher in the atmosphere than the cosmic ray shower. When viewed in the focal plane of a telescope, these two differences result in more compact images that are oriented towards the source location. Figure 2.3 shows the showers of

Figure 2.2 projected onto the focal plane of the Whipple 10m camera with the source located at the center of the field of view.

The first departure from looking for a simple directional anisotropy began in 1982 as the Whipple Observatory sought to exploit these differences in image characteristics to reject the cosmic rays. [38] A camera of 19 PMTs with 0.5° spacing replaced the single PMT so that a crude image of the Cherenkov shower could be recorded. When it was verified that imaging of the showers was possible, the camera was expanded to 37 PMTs. Using the differences between gamma-ray and cosmic ray images to reject background, the Crab Nebula was detected at the 9cr level in data taken between 1986 and 1988. [67] This was the first undisputed detection of TeV gamma-ray emission identified with a source. With the successful detection, the camera was again upgraded in 1988 to a camera of 91 1" PMTs with 0.25° spacing surrounded by 18 2" PMTs. The sensitivity of this imaging camera was a factor of 100 better than a camera with no background rejection. [38] Data taken with this camera and slight variations of it form the basis for this work. During the 1988/89 observing season a substantial database was compiled for the Crab Nebula. From this database, an image selection technique based on the elliptical Hillas parameters [30] of each event was developed. This technique, called "Supercuts", was used to detect the Crab Nebula at the 34

2.1.2 Current State of VHE Gamma-ray Detectors

Since the establishment of the imaging technique, many candidate sources of TeV gamma-ray emis­

sion have been observed with the Whipple 10m telescope. It was not until 1992 that another source, the AGN Markarian 421 [53], was detected. Since then the TeV gamma-ray catalog has grown to 7 sources including both northern and southern hemisphere objects. Table 2.1 lists the TeV gamma-ray sources in order of detection; Table 2.2 lists the current TeV imaging experiments and the sources which they have detected. ' The detection does not have the full significance associated with 34

(a) 0.35 TeV Gamma (a) 1.00 TeV Proton !"" 1 22 I M I I I I I I I I 'I I M I I I I I

20

18

H i-

'•A ' 16 y

JdE •ou 3

> •-

I I I I I r I t I I I I I I I I I I I -1000 -500 0 500 1000 -1000 -500 0 500 1000 X position (m) X position (m)

Figure 2.2 Side views of a 0.35 TeV gamma-ray shower (left) and a 1.00 TeV cosmic ray shower (right). The energies are chosen such that roughly equal amounts of total light would be detected by a detector like the Whipple 10m telescope. Notice that the gamma-ray shower has much less transverse momentum and initiates much higher in the atmosphere than the cosmic ray shower. 14

(a) 0.35 TeV Gamma (a) 1.00 TeV Proton

OiM bO 2, 3 sCA CO o O o O a a.

0 1 2 0 1 2 X position (deg.) X position (deg.)

Figure 2.3 Light detected in the focal plane of the Whipple 10m telescope from a 0.35 TeV gamma-ray shower (left) and a 1.00 TeV cosmic ray shower (right). Notice that the gamma-ray shower is much more compact and oriented towcirds the center of the camera than the cosmic ray shower. 15

Table 2.1 Current catalog of detected TeV gamma-ray sources.

Year Energy Source Detected Threshold Level Group Reference Crab Nebula 1986-88 0.7 TeV > lOo- Whipple Weekes et al. [67] Markarian 421 1992 0.5 TeV > lOo- Whipple Punch et al. [53] PSR 17Q6-44 1992-93 1.0 TeV > lOtr CANGAROO Kifune et al. [35] Markarian 501 1995 0.3 TeV > lOo- Whipple Quinn et al. [55] lES 2344 1995 0.3 TeV 4cr Whipple Not published Vela Nebula 1996 1.0 TeV la CANGAROO Yoshikoshi [73] GRS 1915-1-105 1996 0.7 TeV 6

It should be noted that TeV gamma-ray astronomy has not been a steady progression of successes. A number of sources were reported as sources of TeV gamma-ray emission in the 1970's and early 80's (e.g. Hercules X-1, Cygnus X-3) which were confirmed by other groups (see Fegan [24] and references therein). However, with the advent of more sensitive imaging telescopes, the gamma-ray nature of these signals is confusing. For example, bursts of ~ ^-hour duration from Hercules X-1 were detected by 3 independent groups [24] in 1986. Two of the groups were sensitive to TeV energies and capable of imaging. The third group was sensitive to PeV energies and could discriminate cosmic rays from gamma rays based on the muon content. All of the observations showed similar periodicity near the binary period and similar power. However, when the showers contributing to the periodic signal were analyzed for their gamma-ray characteristics, they looked more like the background cosmic ray showers. With the exception of the Crab Nebula, observations with the 109 PMT camera by the Whipple group have failed to detect any emission, steady or periodic, from Hercules X-1 or any of the other sources of TeV emission reported before 1989.

2.2 Markziriein 421

As mentioned earlier, the large number of AGN detected by EGRET has turned the focus of TeV gamma-ray astronomy towards extragalactic objects. Since this research focuses on the AGN Markarian 421, some background on this object is appropriate. Here I give a brief chronological description of the "discovery" references for Markarian 421 in different energy regimes followed by some important measurements of its associated galaxy.

Markarian 421 was first identified as a galaxy of visual magnitude 13.1 in 1966 by Zwicky [75] in the Catalogue of Gala.xies and Clusters of Galaxies. This is a catalog of galaxies complete to mp=+lo.o. 16

Table 2.2 Atmospheric Cherenkov Imaging Gamma Ray Observatories as of 1996 and the sources which each have detected. Sources where a DC excess was detected are included. Sources with only periodic emission are omitted. Organization Site Long. Lat. Elev. Threshold Sources (deg.) (deg.) (km) (TeV) CANGAROO Woomera, 137E 31S 0.0 1.0 Crab,Vela, Aust. PSR1706 Durham Narrabri, 145E 31S 0.2 0.1 Only periodic sources Aust. CAO,Ukraine Crimea 34E 45N 2.1 1.0 Crab Lebedev, C.I.S. Tien Shan 75E 42N 3.3 1.0 Crab,Mrk421 HEGRA La Palma, 18W 29N 2.2 0.5 Crab,Mrk421, Spain Mrk501,GRS1915 Whipple Arizona lllVV 32N 2.3 0.2 Crab,Mrk421, Mrk501,lES2344 C.A.T., France Pyrenees IW 43N 1.5 0.2 Crab,Mrk421, MrkSOl TACTIC Mt. Abu, 73E 24N 1.7 0.2 Not fully operational India Telescope Array Utah 40N 113W 1.3 1.0 Not fully operational

Markarian 421 is listed only by its right ascension and declination on survey plate 731. No radial velocity is given, and no identification with NGC or IC catalog objects is listed. Other than being identified as

"extremely compact", Markarian 421 has no distinction in the catalog. Observations to find galaxies with ultraviolet continua were made from 1965-1970 at the Byurakan Observatory with a 1.5° prism mounted on a 40" Schmidt telescope. The name "Markarian 421" is

derived from being the 42P' object on this list which was produced by the Russian astronomer B.E. Markaryan. [45] He describes this object as follows:

Condensed spheroidal galaxy with ill-defined edges. An 18"* satellite in contact at NE. Seyfert features possibly present. Ha reliably present in the spectrum.

Markarian 421 is further described as "sle" where the "s" indicates a spectrum similar to that of quasars. As such, the ultraviolet emission is considered to be of non-stellar origin. The "1" indicates strong continuum emission and "e" denotes the presence of emission lines [Ha and/or Hp) in the spectrum. It is listed as having a magnitude of 13.5. In 1973, Markarian 421 was ne.xt identified as the radio source B2 1101+38 in the 2"'' Bologna Catalogue. The third section of this catalog contained 3227 sources of 408 MHz radiation detected 17

above 0.2 flu.x units by the Bologna Northern Cross telescope. Observations were made in the late 1960's and early 1970's between +34®02' and +40° 18' latitude. Markarian 421 appears to be an average object in this catalog with a peak flu.x of 1.15 Jy.

Unlike its non-descript detections at lower energies, Markarian 421 was first detected as a transient X-ray source by the Leicester University Sky Survey Experiment on the Ariel V satellite. Ricketts, Cooke and Pounds [57] report 'a particularly interesting first e-vamp/e'of high galactic latitude transient

X-ray sources. They describe observations of a previously unreported 2-18 keV X-ray source in Ursa Major which they label A1103+38 and give a probable identification with Markarian 421. The initial observation from 3-6 May 1975 gave a 3«r detection at 1.2 cts/s. During a subsequent 9-day observation only a la upper limit at 1 ct/s was established. However, observations from 22 May to 1 June 1975 showed a steadily increasing intensity up to ~16 cts/s on 28 May and then an irregular fading over the next 4 days. During the fading period a 1 day flare was observed where the intensity doubled. This object is labeled as 2A1102+384 in the 2A Catalogue [19] which is a complete all-sky survey of 2-18 keV

sources. Emphasis is given to high galactic latitudes to concentrate on potentially extragalactic objects. George, Warwick and Bromage [29] studied the 2-6 keV X-ray and ultraviolet observations made

by EXOSAT and lUE during 1984-85. By making flux and spectral measurements they found evidence that the X-ray flux was a superposition of two different components of emission. When the X-ray flux was low, the flux and the spectral index were well correlated in that as the flux increased, the spectrum hardened. However, during a outburst in December 1984, the X-ray flux flared for a period of three days while the spectral index remained constant at ~ 1.

Shortly following the launch of the Compton Gamma-Ray Observatory in 1991, Markarian 421 was detected at GeV gamma-ray energies by the EGRET detector. [65] Object 2EG J1104+3812 in the 2"''

EGRET Catalog was confidently identified as the AGN Markarian 421. There is no strong evidence for flu.x or spectral variability. It is the weakest of the 50+ AGN that EGRET has detected with a flux above 100 MeV around 15 x 10~® photons/cm-/s. Interestingly, it is also the closest AGN detected by

EGRET. As the Whipple Observatory started observing EGRET sources, Markarian 421 was detected in 1992. [53] An average flux above 0.5 TeV of 1.5 x 10~^' photons/cm-/s was detected at the Qc level.

Variability at TeV energies has been routinely observed [61] with dramatic outbursts reported by Ker-

rick et al. [34] and Gaidos et al. [26]. In the flare reported by Gaidos et al., the TeV gamma-ray flux above 350 GeV increased a factor 50 above the quiescent level with a doubling time of 1 hour.

While not "discoveries" of Markarian 421, three other observations are worthy of mention. Com­ 18

parisons of optical, infrared and radio observations by Ulrich [66] in 1975 confirmed that the optical

emission is indeed nonthermal. Ulrich found that the ultraviolet radiation from the elliptical galaxy housing Markarian 421 was linearly polarized. This is generally attributed to synchrotron radiation from charged particles spiraling in a magnetic field. The emission from the central nucleus of the gala.xy

was substantially brighter than the surrounding gala.xy making spectrographic measurements of the galaxy diflBcult. In contrast to Markaryan, Ulrich found no clear evidence for Ha or emission lines

in the spectrum. However, the H- and K-lines of Call and the G-band in absorption were measurable allowing for a redshift of r = 0.0308 to be determined. Besides measuring the redshift Ulrich noticed

the resemblance of B2 1101+38 to the class of galaxies of the prototype BL Lac. These are luminous galaxies with strongly variable nonthermal nuclei. They are also characterized by the lack of bright emission lines in their spectra, strong and variable polarization, and fiat high-frequency radio spectra. Xie et al. [72] made B-band optical measurements of Markarian 421 during 1985-86. On 13 January 1986 they observed the magnitude change from 15.7 to 14.3 over a period of ~ 2.5 hours. Since the

optical emission originates from the nucleus, it is possible to derive an estimate of the black hole mass. The minimum characteristic timescale for large amplitude variations is on the order of an orbital period. For a Schwarzschild black hole of mass M, r = 6GM/c-. Thus,

seconds (2.1)

which gives a black-hole mass for Markarian 421 of

M ~ 1.8 X lO^Me (2.2)

Zhang and Baath [74] made measurements at 6cm with the VLBI between 1980 and 1984 and found a core-jet structure in Markarian 421. During the four observing periods two different blobs appeared in the jets. By measuring the position of these blobs Zhang finds evidence for superluminal motion with apparent transverse speeds ranging from /?app = l-24c to l3app = 1.92c. The suggested viewing angle relative to the jet axis is 34®. Although larger than for most BL Lacs, it should be noted that this measurement is difficult for Markarian 421, and this number may well be revised later. Figure 1.1 summarizes most of the published observations of Markarian 421 since 1977. The flux times the frequency is plotted as a function of frequency such that the area under the curve represents the power radiated at that energy. It is interesting to note that nearly half of the total power radiated by

Markarian 421 is at gamma-ray energies (E> 100 MeV). Observations made by the Whipple observatory are the most sensitive above 200 GeV. As the Whipple observations are the focus of this research.

Chapter 3 gives a description of the telescope and data analysis. 19

3 DATA ACQUISITION AND PREPARATION

Past discussions of the data acquisition and analysis procedures used by the Whipple Observatory

Collaboration, [52], [56], [47], concentrated on the 1988/89 observing season. Many aspects of the Whipple 10m telescope (see Figure 3.1), data acquisition, and data reduction have since changed. Here

I give a description of the current state of the Whipple 10m (hereafter, the 10m) telescope operation, data reduction and analysis focusing on the 1995/96 observing season.

3.1 The Telescope

During the 1988/89 observing season, the 10m operated with a camera consisting of 109 fast pho- tomultiplier tubes (PMTs). There were 91 1" PMTs, with tube center spacing of 0.25°, positioned on a hexagonal grid surrounded by 18 2" PMTs. The hexagonal mirror facets that compose the reflector dish had just been re-coated with a process developed by Liberty, spec. 150 [47]. This used aluminum with a silicon dioxide overcoating.

In 1993, the camera was rebuilt with the outer 18 2" PMTs being replciced with 1" PMTs, and the tube spacing increased to 0.259°. Figure 3.2 shows the cameras from the 1988/89 and 1995/96 observing seasons. More importantly, light cones have been added to funnel light that would fall between the PMTs onto the photo-cathodes. As discussed in Section 4.2, this lead to an increase of 27% in light collection efficiency.

In 1994 a new technique developed by the Fly's Eye group was used to re-coat the mirrors. Instead of the silicon dioxide coated aluminum of Liberty, an anodized aluminum coating 1700A thick is now used. This is more durable, has better reflectivity in the ultraviolet region, and can be done in house. The electronics from the PMT to the analog to digital converters (ADCs) have changed as well.

Figure 4.2 shows a schematic of the current signal path. The biggest change is the addition of a 50n terminator at the base of each PMT. Since the circuit is terminated to 50fi inside the electronics room, the added terminator siphons off ~50% of the current that comes from the PMT. This means that the PMTs can be run at a higher voltage, leading to sharper pulse rise times, without saturating the ADCs. 20

Figure 3.1 Whipple lOm Telescope in its stowed position.

Corresponding to the addition of the 50J2 terminators, the high voltages were increased by ~100V.

3.2 Observing Modes

The way candidate gamma-ray sources are observed has changed as well. In 1988/89, the dominant mode of observing was the so-called ON/OFF mode. In ON mode, data was taken with the telescope pointed at a tentative source for a set amount of time (typically 28 sidereal minutes). OFF data is then taken for the same sidereal duration with the telescope offset in right ascension such that the same area on the sky was re-observed. OFF data was taken to measure the background. The only exception to this procedure occurred when the weather was poor, where changing sky conditions made OFF source observations pointless. During 1993, the so-called tracking or "discovery" observing mode was used more frequently. In this mode, the source region is still observed in the same manner as in ON/OFF mode, but no OFF data is taken. This mode was adopted to increase the on-source coverage of various objects that were being observed. When looking for a gamma-ray signal, it is possible to use a region of parameter space where you do not expect a signal as a measure of the background. [12] The "discovery" mode name 21

The 1988/89 camera for the Whipple 10m telescope

The 1995/96 camera for the Whipple 10m telescope

Figure 3.2 Whipple 10m Telescope cameras for the 1988/89 (top) and 1995/96 (bottom) seasons. Notice that for the 1995/96 camera, the outer 18 2" PMTs have been replaced with 1" PMTs and light funnels have been added to collect the light that would have fallen between the PMTs. 22

was adopted because a tentative source would first be observed in this mode. If anything promising appeared, it would be re-observed in ON/OFF, or "confirmation", mode to verify the presence of TeV gamma rays.

After the discovery of Markarian 421 in 1992 [53], it was routinely observed in ON/OFF mode. During May 1994, a large outburst of TeV photons was observed over a 2 day period. [34] With the discovery of time variability from Markarian 421, much of the future observations of this object were

taken in tracking mode to increase the coverage and better map out the light curve at TeV energies. Consequently, there is relatively little ON/OFF data for Markarian 421 during the 1995/96 observing

season. Except for rare circumstances like the Flare on 7 May 1996, only data taken in ON/OFF mode is suitable for spectral work.

3.3 Data Acquisition and Storage

The data acquisition has undergone significant changes since the 1988/89 observing season. As the

majority of the changes are of an organizational nature and have no direct effect on the 10m telescope sensitivity, I will give brief descriptions of the changes. Rose et al. [58] and references therein give a more complete description of the current data acquisition system. During the end of the 1993/94 observing season, the thresholds on the discriminators that determine when to trigger the telescope were steadily reduced. One major result is an increase in event rates. It was found that as the rates approached ~20Hz the fluctuations became non-Foissonian, indicating that the data acquisition system was saturating. Also, another imaging telescope was installed on the

mountain in 1991 which was intended for stereo observations. To accommodate the higher event rates from lowering thresholds and taking stereo observations, the data acquisition system was completely rebuilt. The only effect on telescope sensitivity when operating just the 10 meter telescope is an increase in the ma.\imum event rate from ~ l5Hz to > 50ffz.

As described by Rose et al. [58], a system based on Hytec List Processor units that communicate with the CAMAC crates was developed. The list processors are programmed to read data from and reset the nearly 20 CAMAC modules. To handle the increase in data written to disk and allow for online monitoring, the Digital Electronics Corporation (DEC) LSI/73 was replaced with a DEC VAX 4000-90. This also allows communication with other PCs which control telescope position, CCD cameras, etc.

The data storage on disk has changed from a simple binary format to the ZEBRA format [14] with different types of events recorded in different records. The bulk of the records are Cherenkov showers recorded in the 10m. For each 24 Cherenkov events, the telescope is triggered at random twice 23

to provide injected pedestal events which serve to monitor the night sky light. Records which have comments entered from the telescope operator regarding the type of run, source, weather, etc. are recorded once or twice per run. Each record is given a universal time stamp with microsecond accuracy.

3.4 Data Reduction

While much about the data structure and cicquisition has changed, little about the data cleaning and

image parameterization has. The most successful and robust technique for detecting TeV gamma rays is "Supercuts" [56] described below and in Section 3.5. Here, the images of the Cherenkov showers on the camera are described by moments, with gamma rays being situated in a narrow region of parameter space. As it is necessary to use ON/OFF pairs for spectral work, the following discussion will be developed in the context of reducing pairs of data. Differences in procedure for tracking data will be noted.

3.4.1 Pedestal Subtraction and Flat-fielding

As in CCD imaging, biases (or pedestals) must be removed and the camera flat-fielded before an image can be analyzed. A set value is added to each PMT signal to allow negative signal fluctuations to be measured. The injected pedestal events mentioned above are used to determine this value for each tube so that it can be subtracted. The RMS deviations of these pedestal events measure the sky brightness. The average pedestal value and RMS deviation are found for each PMT using;

(3.1)

(3.2)

where N is the number of injected pedestal events and pij is the ADC counts in PMT i for event j. Before parameterizing the images, it is necessary to flat-field the camera. Whereas the pedestals are

injected into each data file, an independent run where the camera is illuminated by uniform, intense flashes from an Optitron Nitrogen pulser is taken. Thus, the gain factors are calculated only once per evening unless the PMT voltages are changed. The pulser is peaked in the blue region of the spectrum

to match the typical Cherenkov pulse. The intensity of the pulser is set such that the average pulse will generate ~700 digital counts from each PMT. Data is taken for 2 minutes with an event rate of l5Hz. While the intensity varies greatly from pulse to pulse, the intensity across the camera is very uniform for a given pulse. 24

The average number of digital counts for eacfi PMT, n,-, is found as is the average number of digital counts in all PMTs, (n,). The gain factors, gi, and gain deviations, gdev,, are then calculated via,

1 ^ m = {riij} = ^ riij (3.3) j=i

, 109 <"•) = logE"' (3.4) ts=l

n - (3.5) ~ «.•

((4) - (n.i)-) 9dev, — (3.6) If

3.4.2 Cleaning

Now that the gain factors, pedestals and pedestal deviations are known, we can "clean" each event to remove noise. Any PMTs with "bad" gains or pedestal deviations are set to zero. "Bad" gains means Tii < 100 or n,- > 1024. "Bad" pedestal deviations means Pdev, < 1-5 or pjev, > 6.5. Having a pedestal deviation below 1.5 means the PMT did not have high voltage applied, whereas a pedestal deviation greater than 6.5 means that a star was in the PMT's field of view. Next, in a technique called "software padding" [13], noise is added to each pixel to account for differences in sky brightness between the ON and OFF sky fields^. Due to the method of determining which pixels are included in the image (described below) and the compact nature of gamma-ray shower images, differences in sky brightness can have adverse affects on the gamma-ray signal. Cawley [13] showed that differences in sky brightness between the ON and OFF regions can lead to statistically significant excesses of events that pass the "shape" parameters {length and width, see Appendix B) leading to spurious gamma-ray signals. Image pixels are those in which the Cherenkov signal divided by the pedestal variance exceeds a given threshold. As described in [13], a brighter region will have larger fluctuations and, therefore, a greater chance of a fluctuation canceling out a small Cherenkov signal. Pixels where this cancellation occurs will be turned "off' and, consequently, give smaller image parameters. Until the development of cameras with large numbers of pixels, padding lamps mounted on each PMT would keep the DC signal constant and thus negate differing sky brightness effects. With larger numbers of smaller pixels it has become diflScult to maintain this practice. Instead, we have taken to adding the noise in software that would have been supplied by the padding lamps, thus the name "software padding".

' Only the brightness fluctuations, and not the actual brightness are important since the PMT signals are AC-coupled. 25

For a given PMT /, the pedestal subtracted signal S can be approximated by

Si = Pd.v. X G(0, l) + Ci + y/Qx G{0,1) (3.7)

where G(0,1) is a random value drawn from a zero mean, unit width Gaussian distribution and C,- is the contribution to the signal from Cherenkov light. The component of the signal due to the night sky

noise is Pdev, x G(0,1). A larger value of Pdcv, means a brighter night sky. To ensure that differences in sky brightness do not contribute spurious gamma-like events, noise is added on a pi.xel-by-pixel basis

to equalize the night sky contribution to the signal in the ON and OFF regions. Take pixel 1 of an event in the ON run for example. After the PMTs with bad gains and pedestal deviations have been set to zero, the pedestal deviations of pixel 1 for the ON and OFF regions are compared. If the deviation of pixel 1 in the ON run is larger, no noise is added and the deviation is unchanged. If the deviation of pixel 1 in the OFF run is larger, noise is added by

Sped, =Si + x/prf.„.(OFF)2-p<,„.(0;V)2 X G(0,1) (3.8)

on the deviation is set equal to that for pixel 1 in the OFF run. Software padding is not used for tracking data. The last step in the cleaning procedure is to determine which pixels to include in the image. As described by Punch et al. [52], a two level threshold based on the pedestal deviations is used. The signal in a PMT after pedestal subtraction and software padding is compared to the pedestal deviation. If the signal is larger than 4.25 times the deviation, it is labeled as "picture" and included in the image. If the signal is less than 4.25 but greater than 2.25 times the deviation and it is adjacent to a "picture" pixel, it is labeled as "boundary" and included in the image. All other pixels are labeled "ofP and are not included in the image calculations. Figures 3.3 and 3.4 show a gamma-ray event and background event at various levels of cleaning.

3.4.3 Parameterization

After the event has been cleaned the Hillas parameters are calculated. These are described both graphically and computationally in Appendix B. The Hillas parameters are various combinations of the zeroth, first and second order moments of the images and can be thought of in terms of ellipses.

Looking at Figure 2.3 one would expect gamma-ray events to be better described by an ellipse than the cosmic ray events. This is indeed the case as seen in Figures 3.3 and 3.4. Table 3.1 shows the parameters that are calculated for each event. 26

After Pedestal Subtraction, Gain Raw ADC Values Correction and Software Padding

000 000 000000 1 000000 000000000 - 000000000 0000000000 0000000000 00000000000 00OO00O0O0© 0000000000 0000000000 -000000(M000 0 -00000000000 0000000000 0000000000 000©©©©©000 000000O0O0O

-1- 000000^0 ©©@@©0 00©Q0© ©00 ©Cji)0

1.6 0 1.6 -1.6 0 After Cleaning

©00 # Picture Q0©©©0 0 Boundary ©Off 0Q00000000 Q0000000(^ Parameter Value 0000000000 Width 0.104° Length 0.268'' 00000®0000 Alpha 2.858'' Distance 0.772° Total Size 263d.c. - 0000O# 000

-1.6 0 1.6

Figure 3.3 Whipple 10m event at various levels of cleaning. This event would be selected as a gamma-ray candidate by Supercuts. 27

After Pedestal Subtraction, Gain Raw ADC Values Correction and Software Padding

000000 0000Q0 000000000 (500000000 0000000000 ©000000000 00000^^0000 ©00000000O0 0000000000 0000000000 -©0000000000 -@00000©0G^ 0000000000 0000000000 0000000000© 00000000000 0a@©^©^© ©©@©00000^ ©00000000 000000 ®0@@Q0 000

-1.6 1.6 -1.6 1.6 After Cleaning

•0« • Picture Boundary I - •@••00 O 000«#0000 OOff J0000000O0 00000000^ Parameter Value 0000000000 Width 0.366° 0 -••000000000 Length 0.683° •000000000 Alpha 47.568° ••••000000 Distance 0.751° •••••@000 Total Size 1244d.c. -1- •00000 0^0

-1.6 1.6

Figure 3.4 Whipple 10m event at various levels of cleaning. This event would be identified as a background event by Supercuts and rejected. 28

Table 3.1 Parameters and units calculated for each event. Parameter Parameter Name Units Name Units Parameters Used in this work width, length deg total signal in event dc alpha, distance deg 3 highest PMT signals dc accumulated live-time sec Universal time (/is) mjd Unused Parameters run number N/A signal cut by cleaning dc event number N/A PMTs cut by cleaning N/A azwidth, miss deg signal in spot dc concentration N/A PMTs in spot N/A radius of peak deg muon veto dc x,y centroid deg elevation, azimuth deg asymmetry N/A 3 highest PMTs N/A a.xis slope, intercept N/A phase sec

3.5 Data Analysis

A standard package, which I refer to as a "quick" analysis, has been written to analyze data for a gamma-ray signal. As I have used results from this quick analysis to select databases for spectral work, a brief description is in order. Again I will give this description in the context of analyzing data taken in the ON/OFF mode. Before any selection is done, distributions oilength, width, alpha, dist and events/minute are plotted to check for any gross errors. If none are detected, each ON/OFF pair is truncated to the same length of time. This can be done using the Universal time stamp of each event, but there were rare occasions where communication with the list processors would fail and small time gaps were introduced in the data. A safer and more accurate way of truncating runs to the same length is to use the accumulated live-time. This is the actual amount of time that the system is active and awaiting a Cherenkov trigger.

Next a dist cut, total signal in event (sire) cut, and software trigger-(n2n

^The telescope is triggered when 2 out of the inner 91 PMTs exceed the threshold set by a discriminator. .•V software trigger emulates this by imposing a minimum value on the number of digital counts in the second highest PMT. See Mohanty [47] for a more thorough description of the telescope triggering. 29

Table 3.2 Supercuts values forl995/96.

Size > 400 digital counts i2n 45 digital counts 0.50' < Dist < 1.0' 0.16° < Length < 0.30° 0.07° < Width < 0.15° 0.0° < Alpha < 15.0°

replaced with 1" PMTs. The size cut and software trigger set the energy threshold above which gamma

rays detected and serve to reject triggers which are not caused by Cherenkov showers. The size cut also eliminates most of the single muon events that are detected because the telescope is operating at

a lower energy threshold than in 1988/89. [11] Finally, length, width and alpha cuts are applied as shown in Table 3.2.

Figure 3.5 shows that Supercuts does indeed select gamma rays. The binned values of alpha are plotted after length, width, dist, size and n2nd cuts have been applied. Because the candidate gamma- ray source is at the center of field of view, one would expect the plot to be peaked at small values of alpha. The significance of the signal is determined by

{N„n-Noj}) (Texc — (3.9) where Non and Nojj are the number of counts which pass all the Supercuts criteria in the ON and OFF data, respectively. Since the number of counts are Poisson distributed, = Non and erijj = For the two plots in Figure 3.5 the significances are 12.5(7 and 32

«5 700 c (U t^600 (4-1 o

§400 iz: 1 t 300 1 1--» I I I 200

100

Q I I I I ' I I I I ' I I I ' I I 'I I ' I I I I I I ' I I I I I I I I I I I ' I I I I I I 0 10 20 30 40 50 60 70 80 90 Alpha

350

250

200

150

100

50

0 0 50 60 Alpha

Figure 3.5 Distribution of alpha values for two different Markarian 421 datasets. The solid line is for the ON run, and the dashed line is for the OFF run. The top plot is 848 minutes of data taken be­ tween December 1995 and February 1996. The bottom plot is 108 minutes of data taken during the Flare on 7 May 1996. For both cases there is a clear excess at small values of alpha. 31

4 GAINS, NOISE AND PE/DC CONVERSION

Any procedure to extract energy spectra must address the detector calibration, i.e., how to determine

the primary cosmic ray energy from the observed image parameters. One detector characteristic that sets the energy scale is the efficiency of converting photoelectrons into digital counts, or the pe/dc. I

have made a direct measurement, described in Section 4.1, of pe/dc=1.05 ± 0.10 for 1995-96, as well as scaling the value measured by Ping Kwok from the 1988-89 season to 1995-96. The scaling technique outlined in Section 4.2 gives a pe/dc value in excellent agreement with the direct measurement.

4.1 Direct Measurement of PE/DC Conversion

Lewis [10] and Kwok [37] first made measurements of the pe/dc in 1987 and 1989. The idea is to directly measure the number of digital counts produced in an analog to digital converter (ADC) for a given amount of photoelectrons coming from the cathode of the PMT. Two quantities must be measured before the pe/dc can be calculated:

1. The current gain of the PMTs, and 2. The transmission of the cabling and electronics between the PMT base and the ADCs

These were measured £ifter the March 1996 darkrun.

4.1.1 Me£isurement of PMT Current Gains

The PMT current gain is the number of electrons produced at the anode for each electron coming from the photocathode. Since the anode current depends on the operating voltage, the current gain will also. However, the current gain is independent of photocathode response, thus, any stable light source can be used to determine the gain.

Figure 4.1 is a schematic diagram of the setup used in the experiment. To find the anode current, la, a green LED was used to illuminate the PMT under normal operating conditions. The voltage drop 32

Voltage to PMT V=4-5V

Light Tight Tube

PMT LED

Signal from PMT

200mV 36 cm full scale

Figure 4.1 Schematic diagram of setup used to measure PMT current gains.

across a Ikfi resistor was measured and Ohm's law

used to calculate the current. The LED intensity was adjusted to give la ~100/iA. To determine the

photocathode current, Ip, the PMT was placed in a base having all the dynodes electrically tied to the anode and a bias of 30V applied. The PMT was then illuminated using the green LED at the same intensity used to determine la- A lOMQ resistor was used to determine the current. Since the internal

impedance of the voltmeter, Ri„t, was lOMQ, R is replaced by

= + =5Mn (4.2)

The current gain is given by U/lp and is shown for 6 representative PMTs in Table 4.1 with the average gain G = (4.9 ± 0.4) x 10®. As a check, the current gains were re-measured after the June darkrun time using a picoammeter to determine the photocathode current with negligible change in the results.

4.1.2 Meetsurement of Signal Transmission

One other quantity is needed to determine the pe/dc: the transmission of the signal from the PMT to the ADC. For the 1995/96 camera, the signal path is shown in Figure 4.2. From the PMT, the signal is terminated oOfi to ground and traverses 198ft of RG58 coa-xial cable to a patch panel in the electronics 33

Table 4.1 Current gains in units of 10® for 6 PMTs. Vop and Gop are the nor­ mal operating voltage and corresponding gain. Giooo and G900 are the gains with the PMTs operating at lOOOV and 900V, respectively.

PMT Vop Giooo Gop Ggoo 1 1000 0.41 0.41 0.18 13 1025 0.36 0.44 0.16 37 880 N/A 0.48 0.57 49 1067 0.33 0.55 0.16 61 990 0.67 0.63 0.29 85 890 N/A 0.43 0.48 <^?) 975 0.44 ± 0.09 0.49 ± 0.04 0.31 ± 0.06

room. In the next ~12 ft of RG174 cable, the signal is terminated 470n to ground, passes through a series capacitor and is terminated 50fi to ground again. After passing through a lOx amplifier, another series capacitor and 120ns of RG174 coax, the current is converted to digital counts in an ADC. To find the transmission, a LeCroy Model IP-2 Instapulser was used to generate a current pulse similar to that caused by a Cherenkov shower. Since the Instapulser generates a voltage pulse, a IkQ resistor was used to attenuate the Instapulser. This is necessary since the circuit impedance is around 25n with the termination at the focus box included and around 50fi otherwise. With this resistor, the percentage difference between the circuit impedance with and without the 500 termination is less than

3%. The signal from the pulser (with Ikfi resistor) is injected into the circuit at the base of a PMT. Instead of the signal being digitized in the ADC, it is fed into an oscilloscope where a photograph is taken of the trace. Then, the signal from the the pulser is fed directly into the oscilloscope, and a

photograph is taken of the trace. The ratio of the areas under the two pulses is the transmission. To measure the areas, the photographs were enlarged and traced onto the same piece of paper. The pulses

were then cut out of the paper and weighed. This method gives a transmission oi T = 3.04 ± 0.15, where the transmission is greater that 1 due to the 10 x amplifier in the circuit.

4.1.3 Calculating the PE/DC

Now that the current gain, G, of the PMT and the signal transmission, T, from the PMT to ADC are known, the pe/dc conversion factor a can be calculated [37] by

-1 a = cx(uoxio-»c).rx(i^) (4.3) 34

Cable Path Type Distance PMT to Patch Panel: RG58 198ft Indoor Patch Panel to Amp: RG174 12 ft Patch Panel Amp to ADCs: RGI74 118ft

PMT 470a 50Q

RG174 Coaxial Cable (120 ns) ADCs

Figure 4.2 Schematic diagram of PMT signal path from the PMTs to the ADCs.

The last factor arises because the ADC converts 256 pC into 1024 digital counts. This gives

a = 1.05±0.10pe/rfc (4.4)

To compare Kwok's value of 1.176 pe/dc for the 1988-89 observing season to Eqn. 4.4 it is necessary

to account for the changes in the camera and operating conditions from 1989 to 1995. The most significant changes are an increase in the average operating voltage of the 10m PMTs and the addition of 50 n terminations at the focus box. In addition, some of the PMTs were replaced with ones which had a higher response to a pulsed green LED. All three of these changes occurred during summer/fall

1994. An increase in the operating voltage of lOOV roughly corresponds to a factor of 2 larger current from the PMT. The average operating voltage of the six PMTs tested here is 975 whereas for the 5 PMTs tested by Kwok it is 900. Thus, one would expect the current pe/dc to decrease by a factor of ~ 1.7. With the addition of the 500 terminators at the focus box, one would expect the pe/dc to increase by a factor of 2 since half of the current is being siphoned off by the terminator. The third change is difficult to quantify because 47 PMTs from the 10m camera were replaced with higher gain PMTs. It is not clear which, if any, of the replaced PMTs were used here or by Kwok. If we assume that the gain matching has no effect, a naive estimate of the 1995/96 pe/dc would be Kwok's value times 2.0/1.7 or 1.38 which is well above the value measured here. 35

Looking more closely, the transmission measured by Kwok was 0.73 whereas it is 0.32 (dividing out

the 10 X amplification) in this work. This agrees with the factor of 2.2 increase predicted above. What is strange is that the gain measured here is 2.5 times the gain measured by Kwok instead of the 1.7

we might naively expect. This indicates that something has occurred during the gain matching that is not easily quantifiable. A more rigorous comparison of the pe/dc measured here and Kw^ok's pe/dc is described in the next section.

4.2 Scaling the PE/DC from 1988-89

While a direct measurement of the pe/dc is not tremendously difficult, it is not trivial either and therefore has not been routinely measured during the past 5 years. Once a direct measurement has been made, however, it is straight forward to scale the measurement to other observing periods using techniques developed by Mohanty [47] and Samuelson [59]. The pe/dc=1.176 measured by Kwok for

the 1988/89 season was scaled to the 1995/96 season as an independent method of determining the

pe/dc and to confirm the direct measurement made in the previous section. I will first look at three different approaches of determining the pe/dc times the reflectivity, or the throughput, for the 1995/96 season and then show how to separate the reflectivity from the pe/dc.

4.2.1 Digital Counts in the Second Highest PMT

Mohanty's scaling technique relies on the integral spectrum of the digital counts in the second highest PMT for each event. The second highest PMT is usually referred to as n^nd- As shown shortly, any of the highest PMTs are usable, but the second highest is chosen since it carries the trigger information as well.^

As discussed by Longair [40], the energy spectrum of the cosmic rays at TeV energies is a power

law with a differential index of -2.65. As shown in Figure 4.3, the spectra of the digital counts in the highest PMTs are also power laws with a differential indices between -2.33 and -2.4. The index is -2.33

for n^nd- Thus, it follows that the number of digital counts of the highest PMTs is a power law in the energy of the incident cosmic ray, i.e., n cc E^.

The number of digital counts in the highest PMTs is proportional to the reflectivity and also to the pe/dc (a). This is because a fractional change in the reflectivity causes the same fractional change in photoelectrons produced by the PMT photocathode. Any change in the pe/dc just scales the number

'The telescope is triggered when any 2 of the inner 91 PMTs exceed a threshold. Thus, the number of digital counts in the second highest PMT contains the trigger threshold information. 36

• -» 1st Highest Tube • -> 5th Highest Tube

^ A A-> 10th Highest Tube • 20th Highest Tube 3.1xl0V""'' S 10 0 1

AAA

V:Vi.Vr

AA 2 3 Digital Counts

• -> 1 St Highest Tube • -» 5th Highest Tube A—> 10th Highest Tube T-> 20th Highest Tube 2 7xl0'*n^"'"^^^ -- l OxlK^-'-^^'

Z 10

2 3 Digital Counts

Figure 4.3 Digital count spectra are plotted for the P', 5'*, lO"* and 20"' high­ est PMTs from each event. Differential (top) and integral (bottom) spectra are shown. The differential spectra are well described by a power law with index -2.33 giving integral spectra with index -1.33. 37

of digital counts. In general, the reflectivity of the telescope is wavelength dependent. However, one

can define an overall reflectivity, r, as a convolution of the mirror reflectivity, R, and the PMT quantum eflBciency, M:

r = J R(X)M(X)dX (4.5)

Thus, one has

Tiond a arE^ (4.6)

and the integral spectrum for n2nd as function of digital counts

F{n) = FoX (4.7)

where n is digital counts.

Figure 4.4 is a simple graphic showing how the to determine the throughput (or) ratio for different seasons which I'll label A and B. The cosmic ray flux does not change from year to year so the number of showers above a given energy is constant. This means that we will detect the same number of events above a given energy so long as we are sufficiently above the region where trigger effects are important. A shower of a given energy will have a second highest PMT value nn on curve A and a value on curve B. Using Eqn. 4.7 one can write

Fi = (4.8)

F, = FBnr^-33

= (4.9)

Some algebra yields Fo (4.10) Fi Using Eqn 4.6 one can find a relation between ni and no as

"1 _ (4.11) which when substituted into Eqn. 4.10 gives Cf / \ (4.12) Fi \aBrB J or equivalently, (4.13) KOtBrB/ VFo/ 38

^2

a. Digital Counts

Figure 4.4 Simple graphic illustrating how to determine the ratio of through­ puts, ar, for seasons A and B. 39

The top plot of Figure 4.5 shows the integral spectra of n^nd (in number of events per second) for zenith runs taken during the 1988-89 and 1995-96 observing seasons. These zenith runs give

(4.14) for the ratio of the 1995-96 and 1988-89 throughputs.

4.2.2 Toteil Size of Shower

A similar method of scaling uses the total size (in digital counts) of the shower instead of nonrf- As shown in the middle plot of Figure 4.5, this is not as clean as using the second highest PMT since the integral spectrum is not well characterized by a simple power law over a large range. It is possible to fit the spectrum over a range small enough that a power law is a good appro.ximation and that avoids both threshold and PMT saturation effects. One such fit is shown by the middle plot in Figure 4.5 giving 1.70 for the ratio of the throughputs.

4.2.3 Compare Total Size of Largest Events

A novel approach developed by Frank Samuelson [59] is to look at the total sizes of the largest events in each run. The incident cosmic ray energies for these events should be the same from year to year. Because the outer 18 PMTs are different in 1995-96 than 1988-89, the total size was calculated excluding these PMTs. It is also important that each dataset be the same duration. Thirty minutes of zenith runs taken throughout each observing season were parameterized and ordered by decreasing event size. The bottom left plot of Figure 4.5 is the log of the size for the n-th largest event from each season versus n. The bottom right plot shows the difference versus n. Restricting the range to ~ 1600 < n <~ 3600 in order to avoid PMT saturation effects (low n) and threshold effects (high n) yields a throughput ratio of lO"'^*^^ = 1.65.

4.2.4 Separating the pe/dc and the reflectivity

It is important to note that the throughput ratios from each method are in excellent agreement. However, only the throughput is determined in the scaling approach. Therefore, it is necessary to quantify the change in reflectivity to isolate the pe/dc. Two changes to the telescope as described in Section 3.1 have affected the reflectivity: 1) the addition of light cones to funnel light falling between the PMTs onto the photocathode, and 2) a different mirror coating process. The change in reflectivity due to the addition of light cones can be found using data taken on 7 June 1996. Two zenith runs were taken, one with and one without the light cones on the camera. 40

10 • -> 1995-96 Data - 2.30x10^^*11' • -> 1988-89 Data - 1.15xlO^*n' CO 1

1

•2

90100 200 300 400 500 600 70080090(DOOO 2000 Digital Counts

*0 1995-96 Data - 1.57xl0°*n 10 1988-89 Data - 7.90xl0^*n' 00

1

10 3 4 Digital Counts

(U

Figure 4.5 Three different techniques of scaling the pe/dc from one epoch to another. The top plot shows the integral digital count spectrum of the second highest PMT in events per second, and the middle plot shows the digital count spectrum of the total size of the shower in events per minute. The bottom two plots show the log of the size of largest events for 1988/89 and 1995/96 (left) and the log of the ratio (right). 41

Since the pe/dc is the same for both of these runs, the ratio of the throughputs will be the ratio of the reflectivities. Thus one can use the scaling techniques from Sections 4.2.1 and 4.2.3 to determine the change in reflectivity due to the light cones directly. Figure 4.6 shows the integral spectrum of n^nd and the ratio of the largest events for the zenith runs with and without cones from 7 June 1996. Both techniques yield 1.27 for the ratio of the throughputs meaning that the light cones increase the number of photons hitting the photocathodes by 27%.

The reflectivity curves for the 1988-89 mirrors and 1995-96 mirrors have both been previously mea­ sured. Processing a large database of simulated gamma rays with the reflectivity and camera configu­ ration appropriate for each season shows an increase in light of 16% from 88-89 to 95-96. Coupled with the increase due to the light cones, the increase in reflectivity from 1988-89 to 1995-96 is 46.9%. Putting everything together,

rgs ,c\ 0:95 = Q88 X -—;— X — (4.15) (gr)95 rs8 = 1.176 X (1.68)-^ X 1.469

= l.03pe/dc which is in excellent agreement with the direct measurement as given in Eqn. 4.4. 42

"O 10 c o • -)• Data w/ Cones - 1.58x10 *n o(U C/3 Ui • Data w/o Cones - 1.15x10 *n 0) & V3Ui

-I 10

-2 10 J I I I I L 90100 200 300 400 500 600 70080090(DOOO 2000 Digital Counts

Tubes Saturated 1

With cones

without cones

2000 4000 N-th Largest Event

Figure 4.6 The top plot shows the integral digital count spectrum for runs taken with and without cones on 7 June 1996. The bottom plot compares the log of the total size for the largest events (left) and the log of the ratio (right) for the same two runs. 43

5 METHOD FOR DETERMINING ENERGY SPECTRA

With a aumber of well established TeV gamma-ray sources, the issue of source characteristics can be

addressed. After identifying an object that emits TeV gamma rays, the next logical step is to determine its energy spectrum. Here I discuss the issues relevant to measuring energy spectra and outline one method that has been developed over the past few years. Mohanty et al. [48] gives a more detailed discussion of this "traditional" method as well as presenting another approach that has been developed in parallel by Hillas. Both methods have been extensively compared and found to give similar results despite using quite different techniques. A third likelihood method has also been developed recently by Biller [5]. A thorough comparison between this likelihood method and the methods discussed in Mohanty et al. is currently underway. I will describe the "traditional" method the context of finding the energy spectrum of the Crab Nebula since it is considered the standard candle of TeV gamma-ray astronomy.

5.1 The Standard Analysis

Three important issues must be addressed before spectra can be extracted from data:

1. What parameter cuts should be used to select gamma rays from the data?

2. How is the energy of the primary gamma ray reconstructed?

3. What is the gamma-ray collection area for the telescope?

Because of the low signal to noise from current TeV gamma-ray sources and since there is no gamma-ray source with a known spectrum, it is difficult to answer these issues experimentally. They are generally addressed by Monte Carlo simulations. A database of 214046 gamma rays ranging from 0.1 TeV to 20 TeV with a -2.4 differential power

law index were simulated using the programs described by Mohanty [47]. The gamma rays were uni­ formly distributed over a circle of radius 300 meters perpendicular to the telescope axis. The average 44

zeaith angle of observations made from Mount Hopkins, AZ^ on the Crab Nebula, Markarian 421, and Markarian 501 is ~20°. Therefore, the simulated gamma rays were inclined 20® relative to zenith.

The Cherenkov photons from each shower are processed through a program that models the Whipple 10m telescope, computing PMT values for each shower in photoelectrons. Using the electronic gain

measurements described in Chapter 4. the PMT values are converted to digital counts. For the 1995/96 Crab Nebula observing season, an electronic gain of pe/dc=1.05 ± 0.10 was used. Next, Gaussian

distributed noise based on the average night sky fluctuations is added to each PMT value. For the 1995/96 Crab Nebula observing season the night sky noise per PMT, as determined from the pedestal

deviations, is 4.29 digital counts. Only PMTs with high voltage applied and that were not turned off in software during analysis were used. Typically 5-10 PMTs are not used due to the 3'"'' magnitude star Zeta Tauri which is in the camera's field of view. Each event is then cleaned and parameterized as described in Chapter 3. Because shower parameters are less distinct at the center of the camera and because showers are truncated when near the edge of the camera, a cut of 0.6® < dist < 1.0° is imposed.

This cut allows a better determination of the primary gamma-ray energy from the image parameters. A software trigger of n^nd > 70 digital counts is also imposed to avoid threshold problems for small showers.

5.1.1 Parameter Cuts

The Supercuts method [52], [56] of selecting gamma rays from data consists of a constant pass band for the parameters length, width, dist, and alpha as shown in Table 5.1. However, as found by Mohanty [47], length, width, and alpha are correlated with the primary gamma-ray energy. Figure 5.1 shows how the parameters scale with energy with Supercuts shown for comparison. Clearly, Supercuts is poor at selecting higher energy gamma rays.

Table 5.1 Supercuts values for 1988/89.

0.16° < Length < 0.30® 0.073° < Width < 0.15® 0.51° < Dist < 1.1® o

o o < Alpha < 15.1®

'The latitude of Mount Hopkins is 32''N. The declinations of the Crab Nebula, Markarian 421 and Markarian 501 are 22°, 38° and 40°, respectively. Therefore, observations are made from ~10° zenith angle down to 40° with an average zenith angle of ~ 20°. 45

^0.3 •3

0.2 i f I i ^ 0.1

Q I I I I ! I I I I I I I I I I 1 I I I I I I I I I I I I 1 I I r r I I -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 1.2 Log(Energy)

^0.4 SO.3 [| j + i + f M 0.2

0.1

I I I I I r I r I I I I I I r r I | | uJ | | i | i_j i_J i i i I i -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 1.2 Log(Energy)

<• ( • < • ( > 1 » 1 . . 1 . . 1 1 t . . 1 1 1 i. J i_ J i_ J L U L -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 1.2 Log(Energy)

Figure 5.1 Average parameter values of simulated gamma rays as a function of the log of the energy where the error bars are standard devia­ tions. The shaded areas denote the pass bands of Supercuts. For width and length, Supercuts' sensitivity to gamma rays decreases markedly with increasing energy. 46

For spectral work, it is highly desirable to be able to select gamma rays over a broad range of energies. It is also important that the selection process have a high, known efficiency. Thus, it is necessary to modify Supercuts to account for the parameters' dependence on the primary energy. One problem in doing this is that the primary energies of showers in actual data are not known. However, we can use the total size of the shower, which is correlated with the energy.

First, the values of the three parameters, length, width, and alpha, are binned by the log of the total size, LogS. The average of each bin is fit with a function of the form

parameter = a + b* LogS + c* (LogS)' (.5.1)

For length and width a uniform band, centered on the parameter fit, is found such that 95% of the simulated gamma rays are contained within the band. For alpha, an upper bound of the form of the fit that passes 95% of the gamma rays is found. Figure 5.2 shows the parameter averages, fits and pass band as a function of LogS as well as Supercuts for comparison. The cuts are shown in Table 5.2 with the fits given in the brackets. These "extended supercuts" pass 90% of the simulated gamma rays when used together.

Table 5.2 Extended Supercuts values for 1995/96 Crab Nebula data. The pa­ rameter fits are shown in the brackets.

1 alpha [ 50.71 — 28.19* LogS + 4.26» {LogSy- ] < 12.10 1 length [ 0.09 + 0.05 * LogS + 0.00 * (LogSy- ] < 0.07 1 width [ 0.14 — 0.06 * LogS + 0.02 • (LogSy- ] < 0.05

Note that the quadratic fit does not match the length and width parameters well at larger values of LogS, mainly due to PMT saturation effects. Because the ADCs are not guaranteed to be linear beyond 1024 digital counts, all PMT values greater than this are truncated to 1024 for both Monte Carlo simulations and data. To verify that the parameters deviate from a quadratic fit due to this truncation, the Monte Carlo showers were reprocessed without truncation. The quadratic fits were then found to be a good match to the Monte Carlo parameter averages up to LogS > 4.5 (See Figure 5.3). The apparent deviation at smaller LogS is misleading because there in only one event in the lowest bin. 47

^0.4 •a ^0.3

0.2

0.1

Q I r r r I I I r I I I I I I I I r I I I I I r I I I I I r I I I I I r I [ I r I I I I I r 2.25 2.5 2.75 3 3.25 3.5 3.75 4 4.25 4.5 LogS

2.25

Figure 5.2 Average parameter values as a function of LogS for the standard analysis. The error in the mean is shown (the highest and lowest bin only have one event). The solid line is the fit and the dashed lines are the pass bands that select 95% of the simulated gamma rays. Supercuts is shown as the shaded region for comparison. The poor fits at larger values of LogS (higher energies) are due to ADC saturation effects. 48

0.4

0.2 ---0-

0.1

0 2 2.25 2.5 2.75 3 3.25 3.5 3.75 4 4.25 4.5 Logs

I—— r-j:.o I I II ' ' I I I ' ' I ' I I I I I I I I I'll I ' I I I I I I I I H 2.25 2.5 2.75 3.25 3.5 3.75 4.25 4.5 Logs

Figure 5.3 Average parameter values as a function of LogS for the standard analysis. The solid circles are with PMTs above 1024 digital counts truncated to 1024 digital counts. The open circles have no trunca­ tion are fit well by a quadratic up to LogS > 4.5. 49

5.1.2 Energy Estimation

Now that we have a procedure for selecting gamma rays, we need to determine the gamma-ray energy. This energy is not known in data so it must be inferred from the image parameters. One would expect the energy to be correlated with the total light in the shower since a higher energy gamma ray

will deposit more energy into the atmosphere. This gives more particles in the shower and, thus, more Cherenkov photons. In addition, the light content of the shower will depend on the impact parameter, or the position of the shower core relative to the telescope. The impact parameter is not directly measured either, but it is correlated with the dist parameter. Thus, one would expect LogS and disi to be reasonable estimators of the primary gamma-ray energy.

A prescription for reconstructing the primary gamma ray energy proceeds by binning all the selected gamma rays above x = log{E/N TeV) = —0.5. It is convenient to use x = log(E/N TeV) where N is an arbitrary normalization energy. This energy will be chosen such that the errors on the flux constant and spectral index are uncorrelated. Unless otherwise stated, I will assume N=l. Bins with more than 16 gamma rays are used to find the estimated energy conversion by minimizing x' = ~ ^)" for

x(LogS, disi) = a + b * LogS + c* dist + d* {LogS)' -F e * {dist)' + f * dist * LogS (5.2)

It is desirable that the energy estimate be bias free, i.e., the average estimated energies of the gamma rays in a bin be equal to the average of the actual energies. To a good approximation, the bias turns out to be linear in the i, i.e..

(x — ?) ~ 5 ftx (5.3)

Therefore, the bias can be removed by replacing x with x — g — fix = x(l — h) — g. This amounts to subtracting g from a and multiplying a,b,c,d,e and / by (1 — h). After adjusting the coefficients of Eqn. 5.2 to remove this bias, a = —3.06, 6 = 1.81, c = —1.98, d = —0.21, e = 0.42, and / = 0.57.

Another approach to estimating the energy and removing the bias was investigated. As a starting point, an energy estimate queidratic in logS was found by minimizing — ^)" for

x{LogS) = a + b* LogS -he* (LogS)^ (5.4)

Again, only gamma rays passing cuts and with x > —0.6 were used. The residual x — x was fit with a quadratic function of dist and the results put in the form of Eqn. 5.2. The events are binned by energy.

The bias, 6, and standard deviation, are found for each bin from

6 (5.5) 50

M , -v2 lx — r) (56) Et=l

where W is the number of events in each bin. The sum over ail bins o{ b- xW +(t- is then minimized

by varying the coefficients of Eqn. 5.2. A relatively bias-free estimate could be found for values of W between 10-30. Results from this method were in good agreement with the first method giving biases less than 0.06 for each bin. The energy resolution described below is similar for each method as well

(o-rei=0.160 for the first method and (rrej=0.156 for the second method).

In an ideal detector one could reconstruct the primary gamma-ray energy with no uncertainty, and the energy resolution function would be

i/;(x — x) = S(x — x) (5.7)

However, depending on the height in the atmosphere of the first interaction, gamma rays of a given energy can have vastly different image characteristics when viewed by a single telescope. A gamma ray that interacts higher in the atmosphere will produce less light on the ground and, therefore, have image characteristics similar to a lower energy gamma ray. Figure 5.4 shows the distribution of the difference of the actual gamma-ray energy, x, and the estimated energy, x, of the Monte Carlos. As with many things in nature, the resolution function for the Whipple 10m telescope is well described by a Gaussian function of the form

i){x -x)= (5.8) with (7-rej=0.16 for the cuts prescribed above.

5.1.3 CoUection Area

According to Mohanty [47], the trigger collection area is given by

Atrigix) = /lo X (5.9) ^sim\X) where x is the log of the energy at mid-bin, ntrig{x) is the number of gamma rays that trigger the camera, ^simix) is the number of gamma rays simulated, and Ao is the area normal to the telescope over which the gamma rays are distributed (here, this is x(300m)- = 2.83 x 10®m-). Atrig(x) is shown as solid circles in Figure 5.5. The open circles represent the cut collection area, j4cut(ar), which is determined by using the gamma rays that pass the cuts developed in section 5.1.1 instead of all triggering gamma rays. Notice the rapid fall in ^cut(-c) at energies above x = 0.5 (~3 TeV). 51

1800

1600

1400

1200

1000

800

600

400

200

0 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 x-x

Figure 5.4 Histogram of the difference between the log of the primary energy, x and the log of the estimated energy, x. Only Monte Carlo gamma rays passing the cuts used in the standard analysis are included. The solid curve is a Gaussian function with o"res=0.16 52

80000

js 70000

S 60000

50000

40000

30000

20000

10000

0 -0.5 -0.25 0 0.25 0.5 0.75 1 1.25 Log(Energy)

Figure 5.5 Collection area as a function of energy for the standard analysis. The solid circles show the trigger collection area while the open circles show the collection area for the simulated gamma rays that pass the parameter cuts. The solid line shows the fit to the cut collection area given by Eqn. 5.10.

To avoid bin to bin fluctuations when calculating the spectrum, the cut collection area (open circles) is fit with a product of two Fermi functions,

f -(x+6)\ / (r-d)\ ^cut(x) = a X ( 1+ e •= 1 xflH-ge j (5.10)

The fit shown in Figure 5.5 is for a = 5.13 x 10'', b = 0.32, c = 0.09, d = 1.15, and e = 0.31.

5.2 The Observations

5.2.1 Data Preparation

In order to use the parameter cuts, energy estimate and collection area to extract an energy spectrum, the data must be prepared in the same manner as the simulations. Table A.l in Appendix A lists the data used in determining the Crab Nebula spectrum for 1995/96. The total on-source observing time 53

is 1319.23 minutes. As in the Monte Carlos, each data event is cleaned and parameterized as described in Chapter 3. A distance cut of 0.6° < dist < 1.0° and a software trigger of n2nd > 70 digital counts are also imposed.

5.2.2 Parameter Distributions for the Data

To verify the accuracy of the gamma-ray shower simulations and detector models, various parameter distributions are plotted in Figure 5.6. All distributions were cut to select gamma-rays using the cuts

developed in Section 5.1.1. The length, width and dist distributions from the data show good agreement with the Monte Carlos. The broader alpha distribution in the data is believed to be due to random tracking errors which are not modeled. The increase of ~ 2° in the width of the alpha distribution is accounted for in the extended supercuts listed in Table 5.2. The x and LogS distributions fall off slightly faster in the data than the Monte Carlos. Since the Monte Carlo gamma rays were distributed with a -2.4 power law, this indicates that the spectral index in the data should be smaller than -2.4.

5.2.3 Spectrum Extraction

An energy spectrum of the form

F{E)dE = Q X E-''dE (5.11)

is assumed for the Crab Nebula, where a is the flux at 1 TeV and E is the energy in TeV. As stated earlier, it is convenient to use x = log{E/N TeV), where N is an arbitrary normalization energy. This energy is chosen such that the errors on a and 7 are uncorrelated. Unless otherwise stated, I will assume N=\. With this substitution, Eqn 5.11 becomes

F{x)dx = N'a X (5.12)

For a given a and 7 the expected number of gamma rays in an estimated energy range, rfx, is

(5.13) where T is the total on-source observation time. A bin size of 1/6"' decade in x is used corresponding to the width of the resolution function (see

Mohanty et al. [48]). The significance of the counts in each bin is

[Non-Maff] ^exc — (5.14) •54

600 fi4i 400 - r+J • 400 — •r 200 - 200 • V 0 1 1 1 1 1 1 1 1 0 f 0.05 0.1 0.15 0.2 0.25 0.1 Width Length

0.6 0.8 1 1.2 1.4 Distance

-0.5 0 0.5 1 1.5 2.5 3 3.5 4 4.5 X = Log(E/TeV) Log(Total-size)

Figure 5.6 Comparison of Monte Carlo and data parameter distributions with gamma-ray cuts applied. (The alpha, length and width distribu­ tions have only the other two cuts applied, e.g., the alpha plot is cut on length and width.) Monte Carlo events are distributed with a -2.4 power law. Both data and Monte Carlo events have a cut of 0.6® < dist < 1.0° to increase the energy resolution. The solid lines and error bars are the data and the squares are Monte Carlos. •55

Contours of Chisquared

2.75

2.7

V»

2.65

2.55

2.5

2.45

2.4

3.7 3.8 3.9 4 4.1 4.2 4.3 4.4 Flux Constant x lo"'

Figure 5.7 Contours of x' for the standard analysis using. The solid contours Indicate an increment of x" by 1. The dashed contour corresponds to an increase of x~ by 2.3 which denotes the statistical error bars. where No„ and Nojj are the events passing cuts in a given bin for the ON and OFF data, and (To„ and (To// are the associated statistical errors. For bins with more than a few counts, Con = and

O-off = \/Noff. a and 7 are found by minimizing x~ for the number of gamma rays in each bin compared to the expected number given by Eqn 5.13. Shown in Figure 5.7 are the contours of x'- Each solid contour represents an increment of x' by one. The dashed contour corresponds to an increase of x" of 2.3 and determines the statistical error bars on a and 7 (see Avni [3]). •56

The best fit values give the spectrum / i-T \ —2.57±0.15±0.05 / L * \ F(E) = (4.03 ± 0.35 ± 0.7) X 10-'(535^) {tT^) (' '5)

with statistical and systematic errors, respectively. A simple power law is an acceptable fit as evidenced

by a x-ld.o.f = 7.02/6. I have set iV=0.9 so that the errors in a and 7 are uncorrelated. The systematic errors are found by increasing and decreasing the overall gain of the telescope by 20% and recalculating the spectrum as described by Mohanty et al. [48].

5.2.4 Calculating Fluxes

Although the VHE spectrum for the Crab Nebula is well described by a simple power law, one expects deviations at higher and lower energies. Thus, it is desirable to calculate flux values that could be fit in conjunction with data taken at other energies. If the spectrum is not dramatically different

from a power law, Mohanty et al. [48] describe a technique where the flu.xes can be explicitly calculated. They find a "modified area" which is a convolution of the collection area and the energy resolution function, i.e.,

.4(f) = F{x)A{x)il>{x — x)dx /F{x) (•5.16)

An iterative approach is used to determine the modified area. Initially, A is calculated assuming the resolution function is a delta function. Next, an approximation to the flux is found by fitting the

data. Then, A is recalculated using the correct resolution function. The last two steps are repeated until convergence. If we assume a power law and use the resolution function given by Eqn. ^5.8, the modified area can be written as

A(x) = ^ •=— / I-"'" A(x) dx (5.17) ^re5 v27r J—00

~ e''-"''(^—^A(io) + ^^^A''(io) + • •-j (5.18)

where Xg =x — (7re,-(7 — 1)- As shown in Figure 5.8, the modified collection area is insensitive to the

precise value of gamma. Thus convergence occurs after one iteration. Once the modified area is known, the flux for a bin with small width is simply

F{E) ~ - (5.19) T A(E) AE where Nexe is the number of excess events in a bin, T is the on-source observation time and AE is the width of the bin. Table 5.3 shows the bin by bin flux values for the 1995/96 Crab Nebula calculated using Eqn. 5.19. The final spectrum is plotted in Figure 5.9. 57

Collection Area

Modified Area

4- I I I [ I I i_J I I III u_i I—L

I 10 Energy

Figure 5.8 The top plot shows the collection area (open circles) and the fit to the collection area given by Eqn. 5.10 (solid line). The dashed line is the modified area using a resolution function of Urei = 0.16. The bottom plot shows how the modified area depends on the spectral

index 7. 58

-5 > (U H C/3 I§

-10

I 10 (E/TeV)

Figure 5.9 Energy spectrum of the Crab Nebula from the 1995/96 observing season. The line is the fit given in Eqn. 5.15.

Table 5.3 Bin by bin flux values for the 1995/96 Crab Nebula database.

X at Collection Modified Flux ±1(T error mid-bin Energy(TeV) Excess Area(m-) Area(m") (s~' m~- TeV~^) -0.250 0.562 683 ± 60 32464 27385 (1.45 ± 1.29) X 10-' -0.083 0.826 513 ±50 47699 43594 (4.66 ± 4.59) X 10-® 0.083 1.211 388 ± 40 49487 53955 (1.94 ±2.03) X 10-« 0.250 1.778 222 ± 33 50023 57152 (7.15 ± 1.07) X 10-® 0.417 2.612 108 ± 26 50349 55905 (2.42 ±6.03) X 10-® 0.583 3.828 109 ± 24 46337 52486 (1.77 ±3.91) X 10-® 0.750 5.623 9± 17 38050 47710 (1.10 ±2.13) X 10-® 0.917 8.260 15 ± 8 27134 41732 (1.42 ±8.35) X 10-1° 59

6 ENERGY SPECTRUM FROM MARKARIAN 421-THE FLARE

On 7 May 1996 the largest flux detected by a ground-based gamma-ray telescope was observed

during a remarkable Flare from Markarian 421. Lasting less than 24 hours, the flux increased to nearly 10 times the steady Crab Nebula flux with a doubling time of ~1 hour. While the time structure is interesting, important questions can be addressed by measuring the energy spectrum. What are the highest detectable energies? Is there any evidence for an energy cutoff and if so, at what energy? Initially, the spectrum of Markarian 421 was extracted using the standard analysis outlined by Mohanty et al. [48] and described in Chapter 5. This analysis employs a dist < 1.0° cut to reject images affected by the edge of the camera. While this cut increases the energy resolution, it also decreases the collection area at higher energies. Therefore, in an extended analysis, this cut was removed and various techniques were employed to raise the collection area while minimizing background. Without the upper distance cut, some events will be severely truncated by the edge of the camera. This truncation

leads to a confusion of the length and width parameters. Thus, it is was necessary to add a cut of alpha < 30.0° to reject these events before developing the cuts. Different methods of fitting the parameters and developing cuts were investigated to determine the highest detectable energy from the Flare and search for a cutoff. In Sections 6.1 and 6.2, I will describe the extraction of the energy spectrum of Markarian 421 during the Flare using the standard analysis. Differences between the Crab Nebula and the Flare will be noted. Then I will detail the various techniques used to investigate the high energy end of the spectrum in Section 6.3.

6.1 The Markariein Flare Spectrum—Standard Analysis

The elevation ranges over which the Crab Nebula and Markarian 421 are observed are very similar for the Whipple 10m telescope. Thus, the same set of simulations described in Chapter 5 can be used here. However, it is necessary to use the telescope gains and average sky noise relevant to the Markarian 421 observations. A value of pe/dc=1.03 is used here. This value was determined by scaling the direct measurement of the pe/dc=1.05 described in Section 4.1 to the night of the flare. The average sky 60

noise per PMT for the Markarian 421 field is 3.60 digital counts. This was determined from the average

pedestal deviation of PMTs that had high voltage applied and were not turned off during analysis. Typically only 1-2 tubes are turned off during analysis as compared to the 5-10 turned off for the Crab Nebula. Each Monte Carlo event is cleaned and parameterized as described in Section 3.4. In addition, a 0.6° < dist < 1.0° cut and software trigger of 70 digital counts are imposed.

6.1.1 Parameter Cuts, Energy Estimate and Collection Area

The procedure to develop parameter cuts, find the energy estimate and determine the collection area are described more fully in Sections 5.1.1, 5.1.2, and 5.1.3. Here I will just quote the results for

the Flare data set. The extended supercuts used to select gamma rays from the Flare data are shown in Table 6.1. After removing the bias, the coefficients of the energy estimate equation are a = —3.60,

Table 6.1 Extended Supercuts values for 7 May 1996 Flare from Markarian 421. The parameter fits are shown in the brackets.

1 alpha [53.56 - ZQA3*logS + 4.71 + (logSy- ] < 12.10 1 length [ 0.10 + 0.05 * logS + 0.00 * [logSy- ] < 0.07 1 width [ 0.23 - 0.12 */O55 + 0.03* < 0.05

6 = 1.82, c = —2.03, d = —0.21, e = 0.42, and / = 0.57. The resolution function is well described by a

Gaussian with o-rej=0.16. The fit to the cut collection area as shown in Figure 6.1 has a = 5.22 x lO"*, b = 0.31, c = 0.09, d = 1.08, and e = 0.32. As one would expect, the cuts, energy estimate and collection area are nearly identical to those developed for the Crab Nebula observations.

6.2 The Observations

6.2.1 Data Preparation

There were no complete OFF runs taken on 7 May 1996 which could be used to subtract the background. Instead, for each ON run, I have chosen five different OFF runs taken during during the

1995/96 observing season. Each OFF run was chosen to have a similar gain and zenith angle as the corresponding ON run. Table A.2 in Appendix A shows which background runs were selected and how they were paired with the ON runs. Each of the five ON/OFF combinations were cleaned and parameterized as described in Chapter 3. All of the runs were then cut to 27 minutes live-time for a 61

80000

« 70000

5 60000

50000

40000

30000

20000

10000

•0.5 -0.25 0 0.25 0.5 0.75 1 1.25 Log(Energy)

Figure 6.1 Collection area as a function of energy for the 7 May 1996 Flare from Markarian 421. The solid circles show the trigger collection area while the open circles show the collection area for the simulated gamma rays that pass the parameter cuts. 62

Table 6.2 Counts for the ON runs and OFF run sets. The average OFF counts, statistical errors of the OFF, and the excess are shown in the last 3 columns. Only bins with x > —0.4 are included in the totals.

X ^Vo//(l) Nof/{2) A^o//(3) iVo//(5) {Noff} (ToJJ Excess{(T) -0.58 157 30 30 41 50 47 40 9.34 7.49 -0.42 424 44 49 77 77 67 63 15.53 14.00 -0.25 464 78 101 85 73 73 82 11.70 15.58 -0.08 367 45 58 45 49 42 48 6.22 15-84 0.08 267 26 24 36 29 41 31 7.12 13.24 0.25 146 24 23 25 29 22 25 2.70 9.77 0.42 96 29 25 10 17 13 19 8.01 6.08 0.58 47 15 11 10 11 14 12 2.17 4.87 0.75 24 8 10 7 8 6 8 1.48 3.13 0.92 11 7 3 4 3 4 4 1.64 1.89 1.08 1 1 2 0 0 0 1 0.89 0.00 Total 1423 233 257 222 219 215 230

total time of 108.0 minutes. A software trigger of 70 digital counts and a 0.6® < dist < l.O® cut imposed as well.

6.2.2 Parameter Distributions for the Data

Various parameter distributions are plotted in Figure 6.2. All distributions were cut to select gamma- rays using the cuts developed in Section 6.1.1. The length, width, alpha and dist distributions from the data show good agreement with the Monte Carlos. The alpha distributions between Monte Carlo and data match much better because the telescope tracking is better for Markarian 421 than for the Crab Nebula. The x and LogS distributions fall off slightly faster in the data than the Monte Carlos. Since the Monte Carlo gamma rays were distributed with a -2.4 power law, this indicates that the spectral index in the data should be smaller than -2.4.

6.2.3 Spectrum Extraction

To extract a final spectrum, all 5 OFF run sets were used to determine the background. For each

bin, the average of the 5 sets was used to subtract background and the deviation was used for

The flux constant, a, and the spectral index, 7, are found by minimizing x' for the number of gamma rays in each bin compared to the expected number given by Eqn 5.13. Shown in Figure 6.3 63

0.05 0.1 0.15 0.2 0.25 O.l Width Length

600 F=

400 - L A

1 - r 200 -

- a

~ r. 1 r 1 1 1 1 1 -•j-i-i-Li.i-i L 40 60 80 0.6 0.8 1 1.2 1.4 Alpha Distance

10^?

10

I I I I I I I I I I I r il I I I I I I I -0.5 0.5 1 1.5 3.5 4 4.5 x = Log(E/TeV) Log(Total-size)

Figure 6.2 Comparison of Monte Carlo and data parameter distributions with gamma-ray cuts applied. The solid lines and error bars are data and the squares are Monte Carlos. The alpha, length and width distributions have only the other two cuts applied, e.g., the alpha plot is cut on length and width. Monte Carlo events are distributed with a -2.4 power law. Both data and Monte Carlo events have a distance cut of 0.6° < dist < 1.0° to increase the energy resolution. 64

Contours of Chisquared

2.66

2.64

2.62

2.6

« 2.58

^2.56

on 2.54

2.52

2.5

2.48

2.1 2.15 2.2 2.25 2.3 2.35 Flux Constant , X 10

Figure 6.3 Contours of x" for the standard analysis. The solid contours indi­ cate an increment of x" by 1. The dashed contour corresponds to an increase of x' by 2.3 and denotes the statistical error bars. are the contours of x' with each solid contour representing an increment of x' by one. The dashed contour corresponds to an increase of x~ of 2.3 and determines the statistical error bars on a and 7 (see

Avni [3]). The final spectrum is

, £ n-2.S6±0.07±0.1 , , s FiE) = (2.24 ±0.12 ±0.7) x 10^ (—j (6.1)

A simple power law is a good fit to the data as shown by a x'/d o f = 3.69/6. The errors quoted are first statistical and then systematic. For the spectral index, an additional systematic error of 0.05 is added. This is difference between the largest and smallest index obtained from doing a spectral analysis using each of the five OFF sets independently. The corresponding difference for the flux constant is small. 65

1 _ 10 (EyTeV)

Figure 6.4 Energy spectrum of Markarian 421 during the 7 May 1996 Flare. The line is the fit given in Eqn. 6.1.

The final spectrum is plotted in Figure 6.4. Table 6.3 gives the fluxes calculated using the modified area described in Section 5.2.4.

6.3 The Extended Analysis-Removing the Upper Distance Cut

The energy spectrum for Markarian 421 appears to be an unbroken power law extending beyond the sensitivity of the Whipple 10m telescope. I will now focus on determining the highest energy above which we can claim a significant detection. While the cuts used in the standard analysis are good for extracting spectra, they are poor for searching for high energy events. This is due primarily to the dist < 1.0° cut. Most of the high energy gamma rays will have large impact parameters, and therefore, large distance values. In this extended analysis, the upper distance cut was removed to increase the sensitivity to higher energy gamma rays. In order to reject events severely truncated by the edge of the camera, a cut of alpha < 30.0° was imposed. This prevents events which have their length and width confused from 66

Table 6.3 Bin by bin flux values for the Flare from Markarian 421.

LogE at Collection Modified Flux ±10" error mid-bin Energy(TeV) E.xcess Area(m-) Area(m-) (s~^ m~" TeV~^) -0.250 0.562 382 ± 24 32437 27218 (9.97 ±6.40) X 10-' -0.08.3 0.826 319 ±20 47378 43521 (3.55 ±2.23) X 10-" 0.083 1.211 236 ± 17 49642 53243 (1.46± 1.10) X 10-' 0.250 1.778 121 ±12 50594 55975 (4.86 ±4.98) X 10-8 0.417 2.612 77 ± 12 49167 54878 (2.15 ±3.54) X 10-8 0.583 3.828 35 ± 7 41660 51860 (7.05 ± 1.45) X 10-8 0.750 5.623 16 ± 5 34769 47290 (2.40 ± 7.66) X 10-9 0.917 8.260 7 ± 3 28265 41068 (8.25 ±4.36) X 10-9

being included in the development of cuts. Apart from the dist < 1.0° cut, poor parameter fits at large values of logS also decrease sensitivity to higher energy gamma rays. I first looked at the effect of removing the upper distance cut. Then, I tried opening up the pass bands, using E to develop cuts, and using more complex fitting functions for the log of the size. I find that quadratic fits in logS for each parameter with pass bands accepting 95% of the simulated gamma rays have the maximum sensitivity to high energy gamma rays. Using these fits and pass bands, the highest energy above which there is a significant excess is ~6 TeV.

6.3.1 No Upper Distance Cut

The parameter fits and the pass bands that select 95% of the gamma rays are shown in Figure 6.6 by the solid and dashed lines, respectively. As is evident from Figure 6.5, Atrig[E) greatly increases without the upper distance cut, especially at higher energies (closed circles). More importantly, the collection area is substantially larger at high energies even after applying parameter cuts (open circles). Using the events which pass the gamma-ray cuts to find x{logS,dist) conversion gives an energy resolution of ffres = 0.22. With the strength of the gamma-ray signal from the Flare, it is useful to use a bin size that corresponds to the energy resolution (see Mohanty et al. [48], Section 2.6). Thus, I will use a bin size of l/5th of a decade hereafter. The number of events passing gamma-ray cuts are shown in Table 6.4 for the ON runs and each of the 5 OFF run sets. There is a clear excess in the bin centered on 5 TeV, with a weaker excess in the bin centered on 8 TeV. 67

X 10^

C 1400

-2 1200

-0.5 -0.25 0 0.25 0.5 0.75 I 1.25 Log(Energy)

Figure 6.5 Collection area as a function of energy for the extended analysis. The solid circles show the trigger collection area while the open circles show the collection area for the parameter cuts that pass 95% of the simulated gamma rays. 68

0.4

0.2

O.I

0 2 2.25 2.5 2.75 3 3.25 3.5 3.75 4 4.25 4.5 Logs

j=0.5

gO.4 nJ 0.3

0.2

O.I

0 2 2.25 2.5 2.75 3 3.25 3.5 3.75 4 4.25 4.5 Logs

—•—- ' V- I I II I I I'll I I I I I I I I 1 I I I I I I I I- I I I I I I ll 2.25 2.5 2.75 3.25 3.5 3.75 4.25 4.5 LogS

Figure 6.6 Average parameter values as a function of LogS for the e.\tended analysis. Errors in the mean are shown, but the highest and lowest bin have only one event. The solid line in the fit and the dashed (dotted) lines are the pass bands that select 95% (99%) of the sim­ ulated gamma rays. 69

Table 6.4 Number of events passing gamma-ray cuts, bin-by-bin, for the ON runs and each of the 5 OFF run sets. The upper distance cut has been removed and the pass band set to accept 95% of the simulated gamma rays. The last 3 columns show the average of the 5 OFF sets, the excess Non — and the significance of the excess (cf. Eqn 5.14). The "Total" row is the sum of the number with x > —0.4.

X Mon ^o//(l) iV,//(3) Noff{5) (Noff) E.xcess -0.5 363 49 52 55 48 58 52 311 15.95 -0.3 473 53 68 75 85 64 69 404 16.27 -0.1 470 69 79 74 71 86 76 394 17.33 0.1 410 74 68 66 67 86 72 338 15.44 0.3 269 44 67 54 67 46 56 213 10.77 0.5 154 36 33 25 22 34 30 124 8.96 0.7 65 24 18 26 23 20 22 43 4.96 0.9 35 16 17 16 12 14 15 20 3.20 1.1 8 7 6 9 11 7 8 0 0.00 1.3 6 3 4 5 2 I 3 3 1.03 1.5 1 0 0 0 0 0 0 1 1.00 Total 1891 326 360 350 360 358 351 1540

6.3.2 Opening Up the Pass Band

While the cut collection area is larger without the upper distance cut, it still drops at higher energies. This is probably due to the fits not matching the parameter averages. Since the gamma ray signal is strong in the actual data, one can require a larger fraction of the simulated gamma rays to pass the cuts. This widens the pass band and will somewhat counteract the deviation of the fits at higher energies. The dotted lines in Figure 6.6 show the pass band that selects 99% of the gamma rays. As 99% of the gamma rays that trigger the camera pass cuts, the cut collection area is nearly identical to the trigger collection area. This collection area does not fall off out to 20 TeV. Although using such a wide pass band does increase the number of gamma rays passing cuts, the signal significance actually decreases because more background is accepted. Shown in Table 6.5 are the bin-by-bin counts and significance. The significance of the bins centered on 5 and 8 TeV have both decreased compared to using the 95% pass band. 70

Table 6.5 Number of events passing gamma-ray cuts, bin-by-bin, for the ON runs and each of the 5 OFF run sets. The upper distance cut has been removed and the pass band set to accept 99% of the simulated gamma rays. The last 3 columns show the average of the 5 OFF sets, the excess Non — and the significance of the excess (cf. Eqn 5.14). The 'TTotal" row is the sum of the number with x > —0.4.

I Non iV.//(l) Ncff{2) iVoy;(3) iVo//(4) iV<,//(5) {Nofj) Excess fere -0.5 475 147 157 158 167 170 160 315 13.34 -0.3 639 208 255 227 236 229 231 408 13.40 -0.1 651 265 274 282 291 271 277 374 13.63 0.1 613 235 281 268 257 298 268 345 10.03 0.3 432 197 214 203 207 189 202 230 10.06 0.5 260 116 135 112 115 113 118 142 7.58 0.7 125 90 64 76 76 79 77 48 3.30 0.9 78 54 49 52 48 37 48 30 2.72 1.1 25 26 28 29 22 24 26 -1 -0.17 1.3 14 11 15 8 9 7 10 4 0.82 1.5 2 1 1 2 0 0 1 1 0.61 Total 2839 1203 1316 1259 1261 1247 1258 1581

6.3.3 Using the x Fits to the Pjirameters

If the average parameter values for alpha, length and width are plotted versus x, we do not see a sharp increase at large values of x as we did for logS. It was thought that developing cuts based on

fits quadratic in x would allow a tighter pass band while keeping the higher energy events. It turns out that the x fits require an even wider pass band since the RMS spread of the parameter values in each bin is larger. (Figure 6.7)

6.3.4 Fitting the Parameters with a Cubic Polynomial

Because the quadratic fits to the parameter values are poor at higher energies the pass bands are

unnecessarily large to pass 99% of the gamma rays. A cubic fit will better match the distributions and, therefore, should decrease the pass band. This is indeed true as seen in Figure 6.7. Using these cuts, the highest energy bin with a marginally significant signal is still centered on 8 TeV (Table 6.6). I have also investigated using cubic fits with pass bands that accept 95% of the gamma rays. While these pass bands increase the significance at lower energies, the significance decreases at higher energies compared to the 99% pass bands. 71

X = Log(E/TeV) Log(Size)

0) 0.4 (U 0.4

2 2.5 3 3.5 4 4.5 X = Log(E/TeV) Log(Size)

0.5 1 3.5 4 4.5 X = LogCE/TeV) Log(Size)

Figure 6.7 Quadratic parameters fits as a function of x (left) and cubic fit to LogS (right) for the extended analysis shown. Here, the error bars are deviations from the average. The dashed lines are the pass bands that select 99% of the simulated gamma rays. Note the better fits at larger values of LogS and ?. 72

Table 6.6 Number of events passing gamma-ray cuts, bin-by-bin, for the ON runs and each of the 5 OFF run sets. The upper distance cut has been removed, the parameters fit with a cubic polynomial, and the pass band set to accept 99% of the simulated gamma rays. The last 3 columns show the average of the 5 OFF sets, the excess Non—{^of j), and the significance of the excess (cf. Eqn 5.14). The "Total" row is the sum of the number with x > —0.4.

X Kn Noffil) ^o//(3) Noff{4) No/fib) Excess <^erc -0.5 498 163 171 176 182 181 175 323 13.66 -0.3 660 217 270 241 259 254 248 412 12.58 -0.1 666 271 288 288 309 297 291 375 12.79 0.1 616 239 292 282 256 297 273 343 9.77 0.3 423 178 192 188 192 175 185 238 10.78 0.5 247 107 110 94 107 100 104 143 8.41 0.7 116 70 56 61 61 66 63 53 4.41 0.9 76 55 47 50 41 44 47 29 2.83 1.1 37 33 38 34 23 32 32 5 0.61 1.3 16 10 15 8 7 3 9 7 1.18 1.5 2 0 1 2 0 0 1 1 0.60 Total 2859 1180 1309 1248 1255 1268 1253 1606 73

6.3.5 Siurunary of Extended Analysis

The cuts that give the strongest high energy signal from Markarian 421 during the Flare use a

quadratic fit to the parameters length, width, and alpha and have a pass band that accepts 95% of the simulated gamma rays. Figure 6.8 shows the flux values using these cuts with the fit derived from the

standard analysis. Figure 6.9 shows the integral significance of the signal versus energy. The spectrum extends smoothly up to 6 TeV with no evidence for a cutoff. Above 6 TeV the statistics are too poor

to draw any conclusions. Now that the spectrum of Markarian 421 during the Flare is known, the rest of the Markarian 421 database from 1995/96 can be analyzed. Of particular interest is whether there is any evidence for spectral variability during periods of high emission and low emission. I address this issue in the ne.xt chapter.

c

10

J L J L 10 (E/TeV)

Figure 6.8 Final energy spectrum of Markarian 421. The flux points are ob­ tained using quadratic tits to the parameters with pass bands that accept 95% of the gamma rays. The solid line is the fit from the standard analysis (see Eqn. 6.1). 1 2 3 45678910_ E/TeV

Figure 6.9 The integral significance as a function of x. The data comes from using quadratic fits to the parameters with pass bands that accept 95% of the gamma rays. The spectrum extends smoothly up to 6 TeV, where statistics run out, with no evidence for a cutoff. 75

7 SPECTRAL VARIABILITY OF MARKARIAN 421

The VHE observations of Markarian 421 strongly suggest that there is little or no constant emission. Instead, we are observing a succession of overlapping flares (cf. Kerrick et al. [34], Gaidos et al. [26], Buckley et al. [9], and Hillas and Skelton [32]) with rise-times typically on the order of a day. With the flux variability of Markarian 421 well established, one wonders if there is similar variability in the spectral index. I have investigated this possibility using the database of Markarian 421 ON/OFF pairs taken during the 1995/96 observing season.

7.1 Choosing the Databases

Excluding data from the night of the Flare, there are 62 ON/OFF pairs suitable for spectral analysis. These were grouped into three databases to investigate the spectral behavior of Markarian 421. All of the ON/OFF pairs were prepared as described in Section 3.4. Then, the gamma-ray rate for each night of observation was determined using the quick analysis described in Section 3.5. As shown in Figure 7.1, a natural break to split the data into a high and low state exists at a gamma- ray rate of 0.8 gammas/min. The 21 pairs from the nights with a rate greater than 0.8 gammas/min are put into the state database. All nights with a rate less than 0.8 but greater than 0.1 are put into the "/otw" state database. The lower cutoff" eliminates those nights with no emission. These just introduce noise causing a decrease in statistical significance. A third set of data which I will refer to as the "combined" database is a combination of the high and low state data. The high and low databases are listed in Appendix A. It should be noted that some of the ON/OFF pairs, when taken by themselves, would fall into a different database. However, I thought it more appropriate to group by nightly rates instead of hourly rates. Table 7.1 shows the results of the quick analysis on all three data sets. 76

Q I I I r I I I I I r I I I I L__] i I I I 1 1 1 1 1 1 1 1 1- 0 0.2 0.4 0.6 0.8 I 1.2 1.4 1.6 Gamma-ray Rate

Figure 7.1 Histogram of the nightly gamma-ray rates for Markarian 421 dur­ ing the 1995/96 observing season. Only data taken in ON/OFF mode in good weather with no indication of telescope problems are included. 11

Table 7.1 Results of the quick analysis for the combined, high and low databases. Database ON Events OFF Events Difference Significance Combined 2038 970 1068 19.47

High 978 346 632 17.37(7 Low 1060 624 436 10.62(r

7.2 Spectral Analysis

As the combined, high and low databases are contemporaneous with the Flare data, the same set of simulations are used here as in the Flare analysis. The parameter cuts, energy estimate, and collection area described fully in Section 6.1.1. The parameter distributions for Monte Carlo and data match well as described previously for the Flare data. Figure 7.2 shows the spectra derived for the combined, high and low databases. Table 7.2 compares the energy spectra derived for these data sets as well as including the results determined for the Flare. In looking for spectral variability, we are not interested in determining the flux constant. Thus, the la- contour of X' is used to determine the error bars on the spectral index. Here, N (cf. Eqn. 5.12) has been chosen to insure that the errors in the flux constant and spectral index are uncorrelated. Systematic errors have not been included since they will affect each of the spectra in a similar fashion.

While the spectral indices are the consistent for the Flare and the high state data, the low state data index is 0.66 smaller than the high state. However, when the error bars for the low state are taken into account, this difference is only a 1.2

Table 7.2 Energy spectra derived for different Markarian 421 data sets taken during the 1995/96 observing season.

Database Energy Spectra xVd.o.f

Combined F(£) = 1.78X10-MO:8#7F)"'''^°" 0.60/6

High F{E)= 2.50 0.20/5

Low F(£) = 1.45x10-^ (5:^)" 0.14/3

7 May Flare F(^)=2.24X10-Mt:JW)~'''"°® 3.69/6 78

-5 > (U H Ui I B ? 3 E

-10

10 (E/TeV)

-5

-10

I - 10 (E/TeV)

Figure 7.2 Energy spectrum of Markarian 421 for the combined database (top) and the high and low databases (bottom). The solid line shows the spectrum for the high state, and the dashed line shows the spectrum of the low state. 79

7.3 Sensitivity to Spectral Cutoff

The Flare results given in Chapter 6 show no energy cutoff up to 6 TeV. However, it is possible that there is a cutoff in the non-Flare spectrum that is intrinsic to Markarian 421. While the derived spectra are consistent with a simple power law, as evidenced by the low x-jd.o.f, I have investigated bow sensitive the spectral analysis would be to a simple power law with a hard cutoff. I divided the 62 OFF runs available for Markarian 421 into two sets. Each set consisted of 31 runs with 853 minutes of data. One set served as the OFF data for spectral analysis. A simulated signal was added to the other set to serve as ON data. Since another set of simulated gamma rays was not available, it was necessary to use the same set of simulations from which the cuts, energy estimate and collection area are derived. Based on the combined spectrum, the only reasonable place that one might be seeing a cutoff is 2 TeV. Thus, I chose to add gamma rays with a -2.4 power law inde.x with a hard cutoff at 2 TeV. The number of gamma rays added was chosen such that the signal to background ratio is similar to that obtained for the high database. The number of events passing Supercuts in the ON and OFF data is 1014 and 437, respectively, with a significance of 15.1

-5 /—S >

-10

1 10 (E/TeV)

Figure 7.3 Energy spectrum of the simulated signal injected into the Markar- ian 421 OFF runs. The lines are fits where all data points are included (dashed) and where only the points below 2 TeV are in­ cluded (solid). Both are good matches to the data. 81

8 CONCLUSIONS

8.1 Results from this Work

Observations of Markarian 421 during 1995/96 provided a rich sample of gamma rays. Flares of unprecedented intensity and short time-scales were observed during May providing the purest gamma- ray sample ever detected with the Whipple 10m telescope. This work presents the VHE spectrum from

Markarian 421 derived from the Flare on 7 May 1996 and also of other data taken throughout the year. Various quantities that characterize the detector were measured for the 1995/96 observing season. The addition of light cones to the PMTs was found to increase light collection by 27%. The direct measurement of the electronic gain of the telescope was in excellent agreement with previous measure­ ments that were scaled to the current season. An analysis of the 1995/96 Crab Nebula database gave an energy spectrum of

/ r, X -2.57±0.15±0.05 / , , \ FiE) = (3.13 ± 0,25 ± 0.7) x 10- (_) "

The errors are statistical and systematic, respectively. This spectrum is in good agreement with that derived by Mohanty et al. [48] from the 1988/89 Crab Nebula observations.

An analysis of the 7 May 1996 Flare from Markarian 421 resulted in a spectrum of

/ IP \ —2.56±0.07±0.l / L J \ /•(B) = (2.24±0.12±0.7).10-«(—) («-2)

An investigation of the high energy end of the spectrum revealed no evidence for a cut off up to 6 TeV. Beyond this energy the statistics are too small to draw any conclusions. DeJager, Stecker

and Salamon [20] tentatively claimed a cutoff above 3 TeV from Markarian 421 based on the results

published in Mohanty et al. [46]. If this cutoff was real, this work shows that it was not due to the extragalactic background light (EBL). MacMinn and Primack [42] have investigated how VHE observations are affected by EBL absorption. Assuming an E~- differential spectrum for Markarian 421, none of their models of gala.xy formation give an absorption cutoff below ~5 TeV. Instead they show that the spectrum steepens above ~0.1 TeV. 82

For cold dark matter models, a spectral index around -2.5 would be observed, whereas the inde.x would

be closer to -2.2 for models including hot and cold dark matter. Even with the strength of the gamma-ray signal from the Flare, the Whipple 10m telescope is not sensitive to an energy cutoff above 5 TeV. However, if the unabsorbed spectrum of Markarian 421 were

known, the spectral index derived in this work could distinguish between the dark matter models of galaxy formation. MacMinn and Primack's results show that the HE spectrum is unaffected by EBL

absorption. Thompson et al. [65] report a spectrum of £—1 i between 0.1-10 GeV for Markarian 421. One possibility is that this simple power law continues up to 10 TeV. If this is true, and if we

assume the spectrum has not changed between 1993 and the night of the Flare, the results of this work support a cold dark matter model of galaxy formation. However, the extrapolation is very large (2^ decades in energy) and other possibilities exist. Clearly, further data covering the energy range from 0.1 GeV to 10 TeV is needed to address this issue properly. The Markarian 421 data taken during the 1995/96 observing season, excluding the 7 May 1996

Flare, were analyzed. The average spectrum was found to be

/ TP \ —2.87±0.30±0.05 / t . \ F(£) = (1.2O±0.25±0.T)xi0-(jj^) {jl^) (")

Dividing the Markarian 421 database into states where the emission was high and low revealed evidence

for spectral hardening during high states at the 1.2tT level. If this is a real effect, correlations with

spectral variability at X-ray and GeV energies might be able to distinguish between hadronic or leptonic jet models for this object. Given the amount of data suitable for spectral analysis, it was determined that the Whipple 10m telescope is not sensitive to a hard spectral cut off above 2 TeV using current analysis techniques.

8.2 Future Directions

Much of the ground work has been laid for making spectral measurements using imaging atmospheric

Cherenkov telescopes. However, current spectral analysis techniques need further improvement. Only data taken in ON/OFF mode is suitable for this technique. As Markarian 421 and other AGN are highly

variable, most observations are carried out in tracking mode to increase on source coverage. Current techniques need to be expanded, as discussed in the following paragraph, to accommodate observations taken in this mode. For the 1995/96 observing season, this would more than triple the amount of

Markarian 421 data available for analysis. It is especially important for weaker sources where long periods of observation are necessary to detect the source at a significant level. 83

The key issue in using traclcing data is finding a suitable method of determining the background.

A technique developed by Lessard et al. [39] to make maps of the gamma-ray sky might provide such a method. If the source is displaced from the center of the camera, it would be possible to monitor the source as well as a background region simultaneously. Another approach would be to use suitably

chosen runs to form a template for background subtraction. The template would be scaled by the relative on and off source observing times. It would be necessary to insure the background runs covered similar zenith angles and had similar gains as the on source runs. A natural extension of this work is to analyze other sources detected with the Whipple lOm telescope.

Markarian 501 is the logical source to study since a substantial amount of data currently exists. In addition, a period of high emission was recently reported by Breslin et al. [8] from the Whipple, CAT and HEGRA collaborations. During this period, both the HEGRA and Whipple groups report a significant excess above 5 TeV. The Whipple observations during this high period range in zenith angle from 20° up to 60°. Krennrich et al. [36] have adapted Supercuts for observations taken at large zenith

angles (>40°). One advantage of this technique is greater sensitivity to gamma rays above 2 TeV than observations taken closer to the zenith, ft is straightforward to adapt the spectral analysis used in this work for data taken at larger zenith angles. This would allow Markarian 501 spectrum to be measured from ~300 GeV beyond 10 TeV.

The more distant future of VHE gamma-ray astronomy looks very promising. The VHE source catalog continues to grow as do the phenomena detected from the extragalactic objects. The current camera on the Whipple 10m is being upgraded to 541 PMTs over the next 3 years. This camera will lower the energy threshold which should lead to detections of more AGN. The increased sensitivity will also lead to either detections or tighter constraints on the gamma-ray emission of SNR. This camera will also provide a more precise estimate of the primary gamma-ray energy. Thus, more precise spectral measurements can be made which implies greater sensitivity to spectral variability. As energy spectra from more AGN are measured, we may begin to constrain the epoch of galaxy formation. If the proposed VERITAS array is approved, it would be possible to do a VHE all-sky survey. Like the HE all-sky survey done by EGRET, we could expect a greater understanding of the high energy behavior of AGN and SNR as well as many new questions to be raised. 84

APPENDIX A CRAB AND MARKARIAN 421 DATABASES

Here I list the databases used throughout this work. All data listed here are taken during the 1995/96 observing season.For spectral work, it is important that as many sources of systematic errors be eliminated. Thus all of the data listed here satisfy the following criteria:

1. Weather conditions are described as optimal in the nightly observer log files, 2. The nightly observers give no indication of problems with the telescope in the log files. 3. No gross errors are detected during the quick analysis described in Section 3.5

1995/96 Crab Database

Table A.l Data runs used to calculate the Crab energy spectrum for 1995/96.

Pair ON Run OFF Run UT Date Duration Nitrogen

1 gtcr003215 gtcr003216 951002 27.00 gtn2003212 2 gtcr003217 gtcr003218 951002 27.00 gtn2003212 3 gtcr003386 gtcr003387 951022 27.00 gtn2003375 4 gtcr003388 gtcr003389 951022 27.00 gtn2003375 5 gtcr003390 gtcr003391 951022 27.00 gtn2003375

6 gtcr003392 gtcr003393 951022 27.00 gtn2003375 7 gtcr003408 gtcr003409 951023 27.00 gtn2003399 8 gtcr003413 gtcr003414 951023 27.00 gtn2003399 9 gtcr003415 gtcr003416 951023 27.00 gtn2003399 10 gtcr003499 gtcr003500 951027 27.00 gtn2003495

11 gtcr003501 gtcr003o02 951027 27.00 gtn2003495 12 gtcr003619 gtcr003620 951117 26.75 gtn2003606 13 gtcr003634 gtcr003635 951118 27.00 gtn20036l8 14 gtcr003648 gtcr003649 051119 27.00 gtn2003637 15 gtcr003668 gtcr003669 951120 27.00 gtn2003660

continued on ne.tt page 85

Table A.l (Continued)

Pair ON Run OFF Run UT Date Duration Nitrogen

16 gtcr003670 gtcr003671 951120 27.00 gtn2003660 17 gtcr003733 gtcr003734 951123 27.00 gtn2003721 18 gtcr003735 gtcr003736 951123 27.00 gtn2003721 19 gtcr003821 gtcr003822 951127 27.00 gtn2003817 20 gtcr003823 gtcr003824 951127 27.00 gtn2003817

21 gtcr003838 gtcr003839 951128 27.00 gtn2003836 22 gtcr003840 gtcr003841 951128 27.00 gtn2003836 23 gtcr003842 gtcr003843 951128 27.00 gtn2003836 24 gtcr003861 gtcr003862 951129 27.00 gtn2003858 25 gtcr003863 gtcr003864 951129 27.00 gtn2003858

26 gtcr003873 gtcr003874 951130 27.00 gtn200387l 27 gtcr004012 gtcr004013 951219 27.00 gtn2004001 28 gtcr004135 gtcr004136 951227 27.00 gtn200413I 29 gtcr004137 gtcr004138 951227 27.00 gtn2004131 30 gtcr004195 gtcr004196 960112 27.00 gtn2004189

31 gtcr004203 gtcr004204 960113 27.00 gtn2004198 32 gtcr004210 gtcr004211 960114 27.00 gtn2004208 33 gtcr004212 gtcr004213 960114 27.00 gtn2004208 34 gtcr004222 gtcr004223 960115 27.00 gtn2004216 35 gtcr004258 gtcr004259 960118 27.00 gtn2004257

36 gtcr004262 gtcr004263 960118 27.00 gtn2004257 37 gtcr004284 gtcr004285 960119 27.00 gtn2004277 38 gtcr004301 gtcr004302 960119 27.00 gtn2004277 39 gtcr004312 gtcr004313 960120 23.48 gtn2004307 40 gtcr004314 gtcr004315 960120 27.00 gtn2004307

41 gtcr004332 gtcr004333 960121 27.00 gtQ2004328 42 gtcr004334 gtcr004335 960121 27.00 gtn2004328 43 gtcr004358 gtcr004359 960124 27.00 gtn2004355 44 gtcr004360 gtcr004361 960124 27.00 gtn2004355 45 gtcr004385 gtcr004386 960126 27.00 gtn2004388

46 gtcr004434 gtct004435 960208 27.00 gtn2004433 47 gtcr004447 gtcr004448 960210 27.00 gtn2004446 48 gtcr004486 gtcr004487 960216 27.00 gtn2004485 49 gtcr004506 gtcr004507 960217 27.00 gtn2004505 86

7 May 1996 Markarian Flare Database

On 7 May 1996 the flux increased by a factor of 50 over the quiescent flux. During this nights observations only TRK runs were taken and, as such, this data would typically be unsuitable for spectral analysis. However, as shown in Figure 3.5, the signal to noise is greater than 90Supercuts. Because of the strong signal I have chosen 5 different sets of OFF data to estimate the background as shown in Table A.2.

Table A.2 Data runs used to calculate the Markarian 421 energy spectrum for the Flare on 7 May 1996. Run I. D. Sidereal Start Pair ON OFF UT Date Duration Nitrogen ON OFF

OFF Set 1 1 gtm4005106 gtm4004621 960312 27.00 gtn2004615 1112 1115 2 gtm4005108 gtm4004516 960217 27.00 gtn2004505 1156 1026 3 gtm4005109 gtm4004720 960320 27.00 gtn2004723 1225 0939 4 gtm4005110 gtm4004808 960326 27.00 gtn2004805 1254 1329

OFF Set 2 1 gtm4005106 gtm4004704 960319 27.00 gtn2004695 1112 1137 2 gtm4005108 gtm4004496 960216 27.00 gtn2004484 1156 1026 3 gtm4005109 gtm4004700 960319 27.00 gtn2004695 1225 0937 4 gtm4005110 gtm4004681 960318 27.00 gtn2004677 1254 0920

OFF Set 3 1 gtm4005106 gtm4004380 960125 27.00 gtn2004372 1112 1110 2 gtm4005108 gtm4004683 960318 27.00 gtn2004677 1156 1022 3 gtm4005109 gtm4004300 960119 27.00 gtn2004277 1225 0937 4 gtm400oll0 gtm4004268 960118 27.00 gtn2004257 1254 0936

OFF Set 4 1 gtm4005106 gtm4004337 960121 23.65 gtn2004328 1112 nil 2 gtm4005108 gtm4004378 960125 27.00 gtn2004372 1156 1007 3 gtm4005109 gtm4004268 960118 27.00 gtn2004257 1225 0936 4 gtm4005110 gtm4004390 960126 27.00 gtn2004388 1254 0930

OFF Set 5 1 gtm4005106 gtm4004304 960119 27.00 gtn2004277 1112 1147 2 gtm4005108 gtm4004339 960121 27.00 gtn2004328 1156 1213 3 gtm4005109 gtm4004306 960119 27.00 gtn2004277 1225 1248 4 gtm4005110 gtm4004140 951227 27.00 gtn2004131 1254 0912 87

1995/96 Markarian Database

The following two tables list the ON/OFF pairs taken on Markarian 421 over the 1995/96 observing season. I have divided the database into 2 sets based on the nightly gamma-ray rate as determined

from a quick analysis (see Section 3.5). To determine an average spectrum for the whole season, both databases are combined. In looking for spectral variability, the high state data (Table A.3) and low state data (Table A.4) were analyzed separately. The rate given for the run is determined from the quick analysis described in Section 3.5. The distinction between the two data sets is described more completely in Chapter 7.

Table A.3 Data runs used to calculate the Markarian 421 energy spectrum when it was in a high state during 1995/96. The Flare on 7 May 1996 is not included. Pair ON Run OFF Run UT Date Duration Rate Nitrogen

1 gtm4004066 gtm4004067 d951222 27.63 0.98 gtn2004045 2 gtm4004264 gtm4004265 d960118 27.62 0.91 gtn2004257 3 gtm4004267 gtm4004268 d960118 27.53 0.91 gtn2004257 4 gtm4004364 gtm4004365 d960124 27.64 1.34 gtn2004355 5 gtm4004366 gtm4004367 d960124 27.01 1.18 gtn2004355

6 gtm4004368 gtm4004369 d96Q124 27.57 1.56 gtn2004355 7 gtm4004370 gtm4004371 d960124 27.17 1.29 gtn2004355 8 gtm4004668 gtm4004669 d960317 27.59 0.83 gtn2004664 9 gtm4004699 gtm4004700 d960319 27.65 1.27 gtn2004695 10 gtm4004701 gtm4004702 d960319 27.64 0.65 gtn2004695

11 gtm4004703 gtm4004704 d9603l9 27.84 1.69 gtn2004695 12 gtm4004719 gtm4004720 d960320 27.62 1.01 gtn2004723 13 gtm4004721 gtm4004722 d960320 27.64 1.27 gtn2004723 14 gtm4004807 gtm4004808 d960326 27.62 0.87 gtn2004805 15 gtm4004809 gtm4004810 d960326 26.98 1.11 gtn2004805

16 gtm4004870 gtm4004871 d960409 27.75 0.97 gtn2004866 17 gtm4005048 gtm4005049 d960422 27.77 0.90 gtn2005047 18 gtm4005133 gtm4005134 d960510 27.77 1.12 gtn2005131 19 gtm4005143 gtm4005144 d960511 27.79 0.83 gtn2005140 20 gtm4005145 gtm4005146 d960511 27.81 0.79 gtn2005140

21 gtm4005162 gtm4005163 d960512 27.70 1.44 gtn2005160 88

Table A.4 Data runs used to calculate the Markarian 421 energy spectrum when it was in a low state during 1995/96.

Pair ON Run OFF Run UT Date Duration Rate Nitrogen

1 gtm4004139 gtm4004140 d951227 27.85 0.54 gtn2004131 2 gtm4004226 gtm4004227 d960115 27.87 0.04 gtn2004216 3 gtm4004228 gtm4004229 d960115 27.79 0.43 gtn2004216 4 gtm4004299 gtm4004300 d960119 27.84 0.04 gtn2004277 5 gtm4004303 gtm4004304 d960119 27.65 0.76 gtn2004277

6 gtm4004305 gtm4004306 d960119 27.62 0.43 gtn2004277 7 gtm4004336 gtm4004337 d960121 23.65 0.08 gtn2004328 8 gtm4004338 gtm4004339 d960121 27.80 0.94 gtn2004328 9 gtm4004377 gtm4004378 d960125 27.74 0.87 gtn2004372 10 gtm4004379 gtm4004380 d960125 27.58 0.25 gtn2004372

11 gtm4004389 gtm4004390 d960126 27.75 0.36 gtn2004388 12 gtm4004391 gtm4004392 d960126 27.75 0.72 gtn2004388 13 gtm4004393 gtm4004394 d960126 27.86 0.75 gtn2004388 14 gtm4004495 gtm4G04496 d960216 27.85 0.39 gtn2004484 15 gtm4004620 gtm4004621 d960312 27.85 0.22 gtn2004615

16 gtm4G04680 gtm4004681 d960318 27.86 0.32 gtn2004677 17 gtm4004682 gtm4004683 d960318 27.85 1.18 gtn2004677 18 gtm4004895 gtm4004896 d960412 27.63 0.58 gtn2004900 19 gtm4004897 gtm4004898 d960412 27.69 0.00 gtn2004900 20 gtm4004906 gtm4004907 d960413 27.77 0.54 gtn2004905

21 gtm4004923 gtm4004924 d960414 27.71 0.40 gtn2004919 22 gtm4004925 gtm4004926 d960414 27.76 0.40 gtn2004919 23 gtm4004939 gtm4004940 d960415 27.68 0.33 gtn2004935 24 gtm4004968 gtm4004969 d960417 27.27 0.00 gtn2004972 25 gtm4004970 gtm4004971 d960417 27.73 0.47 gtn2G04972

26 gtm4004981 gtm4004982 d960418 27.83 0.43 gtn2004985 27 gtm4004987 gtm4004988 d960418 27.77 0.00 gtn2004985 28 gtm4004989 gtm4004990 d960418 27.77 0.43 gtn2004985 29 gtm4005017 gtm40050l8 d960420 27.61 0.54 gtn2005019 30 gtm4005024 gtm4005025 d960420 27.77 0.40 gtn20050l9

31 gtm4005035 gtm4005036 d960421 27.78 0.86 gtn2005033 32 gtm4005039 gtm4005040 d960421 27.77 0.11 gtn2005033 33 gtm4005061 gtin4005062 d960423 27.78 0.43 gtn2005060 34 gtm4005187 gtm4005188 d960514 27.78 0.65 gtn2005185 35 gtm4005202 gtm4005203 d960515 27.77 0.22 gtn2005201

continued on next page 89

Table A.4 (Continued)

Pair ON Run OFF Run UT Date Duration Rate Nitrogen

36 gtm4005236 gtm4005237 d960517 20.71 0.24 gtn200o233 37 gtm4005250 gtm4005251 d960518 27.70 0.43 gtn2005248 90

APPENDIX B CALCULATION OF THE HILLAS PARAMETERS

Simulations done by Hillas [30] showed that gamma rays have distinct images when compared to

cosmic rays. He proposed a set of parameters that could be used to distinguish a gamma-ray signal from the dominant background. Referred to as the Hillas parameters, they are shown graphically in Figure B.l.

Center of field of view

Figure B.l Graphical representation of the Hillas parameters calculated for each event.

The parameters length, width, alpha and dist are used in Supercuts and extended supercuts. Asymmetry can be used to determine if the cometary tails associated with the image are directed toward or away from the source location in the camera. It is not particularly useful due to the small field of view of the current camera. Azwidth is often used when looking for a periodic signal since it retains a larger percentage of the gamma rays although at the expense of increased background. 91

The formulae used to calculate the various image parameters are given below, a;,- and tji is the

position of PMT i in the camera in degrees, s,- is the signal in PMT i. Sums are over all PMTs in the camera.

The first, second and third moments of the images are defined as:

(^> = Si Xi (y) = Si2/t IT Si

Six'f SiUt

(.3) = 2^ = (xy-^> = Si The spread of the moments is then given by:

o-r' = - {y)'

(Try = (xy) -(x) (y)

0-^3 = {x^) - 3 (x-)(x) + {xf = (y^) -3 (jr> (y) +{yf = {x-y} -(x-) (y) (Txy^ = (xy-> - (x) (y2)

-2 (xy) (x)+ 2 (x)- (y) -2(xy) (y) +2(x) (y)"

Now for a few more definitions.

1(1/2) d — (Tyl (7^3 i = [rf2+4(

tan{) = [d -f r) (y) + 2) + 3)

2

Finally, the Hillas parameters are calculated as follows.

[<7,2 + (Tyl + LENGTH

(1/2) WIDTH =

DIST =

(1/2) M/55 = [^l(«(r>= + ,;(y>=)-^Hf£E.^)Mj

mtss SIN{ALPHA) = distance (1/3) ASYMMETRY = length 21 (1/2) (x)- (y^) - 2 (x) (y) (xy) + (x-) (y)' AZWIDTH = (DISTANCEf 92

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